Publications

2015

• Interface Motion in Random Media
  
  • Bodineau T.
  • Teixeira A.
  Communications in Mathematical Physics, Springer Verlag, 2015, 334 (2), pp.843 - 865. (10.1007/s00220-014-2152-4)
  DOI : 10.1007/s00220-014-2152-4
• Numerical study of a cylinder model of the diffusion MRI signal for neuronal dendrite trees
  
  • van Nguyen Dang
  • Grebenkov Denis S
  • Le Bihan Denis
  • Li Jing-Rebecca
  Journal of Magnetic Resonance, Elsevier, 2015, 252, pp.103-113. (10.1016/j.jmr.2015.01.008)
  DOI : 10.1016/j.jmr.2015.01.008
• Path-dependent equations and viscosity solutions in infinite dimension
  
  • Cosso Andrea
  • Federico Salvatore
  • Gozzi Fausto
  • Rosestolato Mauro
  • Touzi Nizar
  , 2015. Path Dependent PDE's (PPDE's) are natural objects to study when one deals with non Markovian models. Recently, after the introduction (see [12]) of the so-called pathwise (or functional or Dupire) calculus, various papers have been devoted to study the well-posedness of such kind of equations, both from the point of view of regular solutions (see e.g. [18]) and viscosity solutions (see e.g. [13]), in the case of finite dimensional underlying space. In this paper, motivated by the study of models driven by path dependent stochastic PDE's, we give a first well-posedness result for viscosity solutions of PPDE's when the underlying space is an infinite dimensional Hilbert space. The proof requires a substantial modification of the approach followed in the finite dimensional case. We also observe that, differently from the finite dimensional case, our well-posedness result, even in the Markovian case, apply to equations which cannot be treated, up to now, with the known theory of viscosity solutions.
• Infinite horizon problems on stratifiable state-constraints sets
  
  • Hermosilla Cristopher
  • Zidani Hasnaa
  Journal of Differential Equations, Elsevier, 2015, 258 (4), pp.1430–1460. This paper deals with a state-constrained control problem. It is well known that, unless some compatibility condition between constraints and dynamics holds, the value function has not enough regularity, or can fail to be the unique constrained viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. Here, we consider the case of a set of constraints having a stratified structure. Under this circumstance, the interior of this set may be empty or disconnected, and the admissible trajectories may have the only option to stay on the boundary without possible approximation in the interior of the constraints. In such situations, the classical pointing qualification hypothesis are not relevant. The discontinuous value function is then characterized by means of a system of HJB equations on each stratum that composes the state constraints. This result is obtained under a local controllability assumption which is required only on the strata where some chattering phenomena could occur. (10.1016/j.jde.2014.11.001)
  DOI : 10.1016/j.jde.2014.11.001
• Optimal Design for Purcell Three-link Swimmer
  
  • Giraldi Laetitia
  • Martinon Pierre
  • Zoppello Marta
  Physical Review, American Physical Society (APS), 2015, 91 (2), pp.023012. In this paper we address the question of the optimal design for the Purcell 3-link swimmer. More precisely we investigate the best link length ratio which maximizes its displacement. The dynamics of the swimmer is expressed as an ODE, using the Resistive Force Theory. Among a set of optimal strategies of deformation (strokes), we provide an asymptotic estimate of the displacement for small deformations, from which we derive the optimal link ratio. Numerical simulations are in good agreement with this theoretical estimate, and also cover larger amplitudes of deformation. Compared with the classical design of the Purcell swimmer, we observe a gain in displacement of roughly 60%.
• Intermittent process analysis with scattering moments
  
  • Muzy Jean-François
  • Bacry Emmanuel
  • Mallat Stéphane
  • Bruna Joan
  Annals of Statistics, Institute of Mathematical Statistics, 2015, 43 (1), pp.323. Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and modulus nonlinearities, which preserves the variance. First- and second-order scattering moments are shown to characterize intermittency and self-similarity properties of multiscale processes. Scattering moments of Poisson processes, fractional Brownian motions, Lévy processes and multifractal random walks are shown to have characteristic decay. The Generalized Method of Simulated Moments is applied to scattering moments to estimate data generating models. Numerical applications are shown on financial time-series and on energy dissipation of turbulent flows. (10.1214/14-AOS1276)
  DOI : 10.1214/14-AOS1276
• Optimal control problems on well-structured domains and stratified feedback controls
  
  • Hermosilla Cristopher
  , 2015. The aim of this dissertation is to study some issues in Control Theory of ordinary differential equations. Optimal control problems with tame state-constraints and feedback controls with stratified discontinuities are of special interest. The techniques employed along the manuscript have been chiefly taken from control theory, nonsmooth analysis, variational analysis, tame geometry, convex analysis and differential inclusions theory. The first part of the thesis is devoted to provide general results and definitions required for a good understanding of the entire manuscript. In particular, a strong invariance criterion adapted to manifolds is presented. Moreover, a short insight into manifolds and stratifications is done. The notions of relatively wedged sets is introduced and in addition, some of its properties are stated. The second part is concerned with the characterization of the Value Function of an optimal control problem with state-constraints. Three cases have been taken into account. The first one treats stratifiable state-constraints, that is, sets that can be decomposed into manifolds of different dimensions. The second case is focused on linear systems with convex state-constraints, and the last one considers convex state-constraints as well, but from a penalization point of view. In the latter situation, the dynamics are nonlinear and verify an absorbing property at the boundary. The third part is about discontinuous feedbacks laws whose singularities form a stratified set on the state-space. This type of controls yields to consider stratified discontinuous ordinary differential equations, which motivates an analysis of existence of solutions and robustness with respect to external perturbation for these equations. The construction of a suboptimal continuous feedback from an optimal one is also addressed in this part. The fourth part is dedicated to investigate optimal control problems on networks. The main feature of this contribution is that no controllability assumption around the junctions is imposed. The results can also be extended to generalized notions of networks, where the junction is not a single point but a manifold.
• Approximate controllability, exact controllability, and conical eigenvalue intersections for quantum mechanical systems
  
  • Boscain Ugo
  • Gauthier Jean-Paul
  • Rossi Francesco
  • Sigalotti Mario
  Communications in Mathematical Physics, Springer Verlag, 2015, 333 (3), pp.1225-1239. We study the controllability of a closed control-affine quantum system driven by two or more external fields. We provide a sufficient condition for controllability in terms of existence of conical intersections between eigenvalues of the Hamiltonian in dependence of the controls seen as parameters. Such spectral condition is structurally stable in the case of three controls or in the case of two controls when the Hamiltonian is real. The spectral condition appears naturally in the adiabatic control framework and yields approximate controllability in the infinite-dimensional case. In the finite-dimensional case it implies that the system is Lie-bracket generating when lifted to the group of unitary transformations, and in particular that it is exactly controllable. Hence, Lie algebraic conditions are deduced from purely spectral properties. We conclude the article by proving that approximate and exact controllability are equivalent properties for general finite-dimensional quantum systems. (10.1007/s00220-014-2195-6)
  DOI : 10.1007/s00220-014-2195-6
• A Holder-logarithmic stability estimate for an inverse problem in two dimensions
  
  • Santacesaria Matteo
  Journal of Inverse and Ill-posed Problems, De Gruyter, 2015, 23 (1), pp.51–73. The problem of the recovery of a real-valued potential in the two-dimensional Schrodinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction of the potential is only logarithmic stable in general. In this paper a new stability estimate is proved, which is explicitly dependent on the regularity of the potentials and on the energy. Its main feature is an efficient increasing stability phenomenon at sufficiently high energies: in some sense, the stability rapidly changes from logarithmic type to Holder type. The paper develops also several estimates for a non-local Riemann-Hilbert problem which could be of independent interest. (10.1515/jiip-2013-0055)
  DOI : 10.1515/jiip-2013-0055
• Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance
  
  • Bonnard Bernard
  • Claeys Mathieu
  • Cots Olivier
  • Martinon Pierre
  Acta Applicandae Mathematicae, Springer Verlag, 2015, 135 (1), pp.pp.5-45. In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal, solution of the Maximum Principle and analyzed with the techniques of geometric control. This leads to a numerical investigation based on so-called indirect methods using the HamPath software. The results are then compared with a direct method implemented within the Bocop toolbox. Finally lmi techniques are used to estimate a global optimum. (10.1007/s10440-014-9947-3)
  DOI : 10.1007/s10440-014-9947-3
• Formal Proofs for Nonlinear Optimization
  
  • Magron Victor
  • Allamigeon Xavier
  • Gaubert Stéphane
  • Werner Benjamin
  Journal of Formalized Reasoning, ASDD-AlmaDL, 2015, 8 (15), pp.1-24. We present a formally verified global optimization framework. Given a semialgebraic or transcendental function f and a compact semialgebraic domain K, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of f over K. This method allows to bound in a modular way some of the constituents of f by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.
• Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation
  
  • Bossy Mireille
  • Champagnat Nicolas
  • Leman Helene
  • Maire Sylvain
  • Violeau Laurent
  • Yvinec Mariette
  ESAIM: Proceedings, EDP Sciences, 2015, 48, pp.420-446. The electrostatic potential in the neighborhood of a biomolecule can be computed thanks to the non-linear divergence-form elliptic Poisson-Boltzmann PDE. Dedicated Monte-Carlo methods have been developed to solve its linearized version (see e.g.Bossy et al 2009, Mascagni & Simonov 2004}). These algorithms combine walk on spheres techniques and appropriate replacements at the boundary of the molecule. In the first part of this article we compare recent replacement methods for this linearized equation on real size biomolecules, that also require efficient computational geometry algorithms. We compare our results with the deterministic solver APBS. In the second part, we prove a new probabilistic interpretation of the nonlinear Poisson-Boltzmann PDE. A Monte Carlo algorithm is also derived and tested on a simple test case. (10.1051/proc/201448020)
  DOI : 10.1051/proc/201448020
• A remark on accelerated block coordinate descent for computing the proximity operators of a sum of convex functions.
  
  • Chambolle Antonin
  • Pock Thomas
  SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2015, 1, pp.29 - 54. We analyze alternating descent algorithms for minimizing the sum of a quadratic function and block separable non-smooth functions. In case the quadratic interactions between the blocks are pairwise, we show that the schemes can be accelerated, leading to improved convergence rates with respect to related accelerated parallel proximal descent. As an application we obtain very fast algorithms for computing the proximity operator of the 2D and 3D total variation. (10.5802/smai-jcm.3)
  DOI : 10.5802/smai-jcm.3
• Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion
  
  • Belaouar Radoin
  • de Bouard Anne
  • Debussche Arnaud
  Stochastics and Partial Differential Equations: Analysis and Computations, Springer US, 2015, 3 (1), pp.103-132. This article is devoted to the numerical study of a nonlinear Schrödinger equation in which the coefficient in front of the group velocity dispersion is multiplied by a real valued Gaussian white noise. We first perform the numerical analysis of a semi-discrete Crank-Nicolson scheme in the case when the continuous equation possesses a unique global solution. We prove that the strong order of convergence in probability is equal to one in this case. In a second step, we numerically investigate, in space dimension one, the behavior of the solutions of the equation for different power nonlinearities, corresponding to subcritical, critical or supercritical nonlinearities in the deterministic case. Numerical evidence of a change in the critical power due to the presence of the noise is pointed out. (10.1007/s40072-015-0044-z)
  DOI : 10.1007/s40072-015-0044-z
• Boundary Integral Equations for the Transmission Eigenvalue Problem for Maxwell’s Equations
  
  • Cakoni Fioralba
  • Haddar Houssem
  • Meng Shixu
  Journal of Integral Equations and Applications, Rocky Mountain Mathematics Consortium, 2015, pp.26. In this paper we consider the transmission eigenvalue problem for Maxwell’s equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission eigenvalue problem as an equivalent homogeneous system of boundary integral equa- tion, and assuming that the contrast is constant near the boundary of the support of the inhomogeneity, we prove that the operator associated with this system is Fredholm of index zero and depends analytically on the wave number. Then we show the existence of wave numbers that are not transmission eigenvalues which by an application of the analytic Fredholm theory implies that the set of transmission eigenvalues is discrete with positive infinity as the only accumulation point.
• Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models
  
  • Haddar Houssem
  • Jiang Zixian
  Inverse Problems, IOP Publishing, 2015. Thin copper deposits covering the steam generator tubes can blind eddy current probes in non-destructive testings of problematic faults and are therefore important to be identified. Existing methods based on shape reconstruction using eddy current signals encounter difficulties of high numerical costs due to the layer's small thickness and high conductivity. In this article, we approximate the axisymmetric eddy current problem with some appropriate asymptotic models using effective transmission conditions representing the thin deposits. In these models, the geometrical information related to the deposit is transformed into parameter coefficients on a fictitious interface. Standard iterative inversion algorithm is then applied to the asymptotic models in order to reconstruct the thickness of the thin copper layers. Numerical tests both validating the asymptotic model and benefit of the inversion procedure are provided.
• On the scaling limits of Galton–Watson processes in varying environments
  
  • Bansaye Vincent
  • Simatos Florian
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2015, 20 (75), pp.1-36. We establish a general sufficient condition for a sequence of Galton–Watson branching processes in varying environments to converge weakly. This condition extends previ- ous results by allowing offspring distributions to have infinite variance. Our assumptions are stated in terms of pointwise convergence of a triplet of two real- valued functions and a measure. The limiting process is characterized by a backwards integro-differential equation satisfied by its Laplace exponent, which generalizes the branching equation satisfied by continuous state branching processes. Several examples are discussed, namely branching processes in random environment, Feller diffusion in varying environments and branching processes with catastrophes. (10.1214/EJP.v20-3812)
  DOI : 10.1214/EJP.v20-3812
• Converse Lyapunov-Krasovskii theorems for uncertain retarded differential equations
  
  • Haidar Ihab
  • Mason Paolo
  • Sigalotti Mario
  Automatica, Elsevier, 2015, 62, pp.263-273. In this article we give a collection of converse Lyapunov–Krasovskii theorems for uncertain retarded differential equations. We show that the existence of a weakly-degenerate Lyapunov–Krasovskii functional is a necessary and sufficient condition for the global exponential stability of linear retarded functional differential equations. This is carried out using a switched system representation approach. (10.1016/j.automatica.2015.09.034)
  DOI : 10.1016/j.automatica.2015.09.034
• Unveiling the Diversification Dynamics of Australasian Predaceous Diving Beetles in the Cenozoic
  
  • Toussaint Emmanuel F.A.
  • Condamine Fabien L.
  • Hawlitschek Oliver
  • Watts Chris H.
  • Porch Nick
  • Hendrich Lars
  • Balke Michael
  Systematic Biology, Oxford University Press (OUP), 2015, 64 (1), pp.3-24. During the Cenozoic, Australia experienced major climatic shifts that have had dramatic ecological consequences for the modern biota. Mesic tropical ecosystems were progressively restricted to the coasts and replaced by arid-adapted floral and faunal communities. Whilst the role of aridification has been investigated in a wide range of terrestrial lineages, the response of freshwater clades remains poorly investigated. To gain insights into the diversification processes underlying a freshwater radiation, we studied the evolutionary history of the Australasian predaceous diving beetles of the tribe Hydroporini (147 described species). We used an integrative approach including the latest methods in phylogenetics, divergence time estimation, ancestral character state reconstruction, and likelihood-based methods of diversification rate estimation. Phylogenies and dating analyses were reconstructed with molecular data from seven genes (mitochondrial and nuclear) for 117 species (plus 12 outgroups). Robust and well-resolved phylogenies indicate a late Oligocene origin of Australasian Hydroporini. Biogeographic analyses suggest an origin in the East Coast region of Australia, and a dynamic biogeographic scenario implying dispersal events. The group successfully colonized the tropical coastal regions carved by a rampant desertification, and also colonized groundwater ecosystems in Central Australia. Diversification rate analyses suggest that the ongoing aridification of Australia initiated in the Miocene contributed to a major wave of extinctions since the late Pliocene probably attributable to an increasing aridity, range contractions and seasonally disruptions resulting from Quaternary climatic changes. When comparing subterranean and epigean genera, our results show that contrasting mechanisms drove their diversification and therefore current diversity pattern. The Australasian Hydroporini radiation reflects a combination of processes that promoted both diversification, resulting from new ecological opportunities driven by initial aridification, and a subsequent loss of mesic adapted diversity due to increasing aridity. (10.1093/sysbio/syu067)
  DOI : 10.1093/sysbio/syu067
• Avis en réponse à la saisine 150519 - dossier C-NL-13-02. Paris, le 7 septembre 2015
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie Anne M. A.
  • Bellivier Florence
  • Berny Philippe
  • Bertheau Yves
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Coléno François
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Eychenne Nathalie
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Jestin André
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie V.
  • Lemaire Olivier O.
  • Lereclus Didier
  • Maximilien Rémi
  • Meurs Eliane
  • Moreau de Bellaing Cédric
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Parzy Daniel
  • Regnault-Roger Catherine
  • Renard Michel
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2015, pp.21 p.. Le Haut Conseil des biotechnologies (HCB) a été saisi le 20 mai 2015 par les autorités compétentes françaises (le ministère de l’Agriculture, de l’Agroalimentaire et de la Forêt) d’une demande d’avis relative au dossier C/NL/13/02 de demande de mise sur le marché de la lignée d’oeillets génétiquement modifiés FLO-40685-1 à des fins d’importation et de commercialisation de fleurs coupées. Ce dossier a été déposé par la société Suntory Holdings Limited auprès des autorités compétentes néerlandaises dans le cadre de la directive 2001/18/CE. Conformément à cette directive, la Commission européenne a adressé le rapport d’évaluation des Pays-Bas ainsi que le dossier du pétitionnaire à l’ensemble des Etats membres. Par cette saisine, les autorités compétentes françaises consultent le HCB au stade ultime de la préparation au vote des Etats membres à la Commission européenne. Le Comité scientifique (CS)2 du HCB a examiné le dossier en séance du 25 juin 2015 sous la présidence de Jean-Christophe Pagès. Le présent avis a été adopté par voie électronique le 7 septembre 2015 et publié le 10 septembre 2015.
• Singular limits for reaction-diffusion equations with fractional Laplacian and local or nonlocal nonlinearity
  
  • Méléard Sylvie
  • Mirrahimi Sepideh
  Communications in Partial Differential Equations, Taylor & Francis, 2015, 40 (5), pp.957-993. We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP equation. This rescaling is based on the exponential speed of propagation of the population. In particular we show that the only role of the fractional Laplacian in determining this speed is at the initial layer where it determines the thickness of the tails of the solutions. Next, we show that such rescaling is also possible for models with non-local reaction terms, as selection-mutation models. However, to obtain a more relevant qualitative behavior for this second case, we introduce, in the second part of the paper, a second rescaling where we assume that the diffusion steps are small. In this way, using a WKB ansatz, we obtain a Hamilton-Jacobi equation in the limit which describes the asymptotic dynamics of the solutions, similarly to the case of selection-mutation models with a classical Laplace term or an integral kernel with thin tails. However, the rescaling introduced here is very different from the latter cases. We extend these results to the multidimensional case. (10.1080/03605302.2014.963606)
  DOI : 10.1080/03605302.2014.963606
• MatVPC: A User-Friendly MATLAB-Based Tool for the Simulation and Evaluation of Systems Pharmacology Models
  
  • Biliouris Kostas
  • Lavielle Marc
  • Trame Mirjam
  CPT: Pharmacometrics and Systems Pharmacology, American Society for Clinical Pharmacology and Therapeutics ; International Society of Pharmacometrics, 2015. Quantitative systems pharmacology (QSP) models are progressively entering the arena of contemporary pharmacology. The efficient implementation and evaluation of complex QSP models necessitates the development of flexible computational tools that are built into QSP mainstream software. To this end, we present MatVPC, a versatile MATLAB-based tool that accommodates QSP models of any complexity level. MatVPC executes Monte Carlo simulations as well as automatic construction of visual predictive checks (VPCs) and quantified VPCs (QVPCs). VPC is a model diagnostic tool that facilitates the evaluation of both the structural and the stochastic part of a model. It is constructed by superimposing the observations over the model simulations while accounting for both the interindivid-ual variability as well as the residual variability. 1 Once underutilized, 2 the VPC now is recognized as one of the most valuable model diagnostics in pharmacological model evaluation. 3–5 Its superiority over comparable diagnostic tools has been established 6 and reflected by the fact that regulatory agencies recommend it as one of the central model diagnostics. 7 (10.1002/psp4.12011)
  DOI : 10.1002/psp4.12011
• Ensuring robustness of domain decomposition methods by block strategies
  
  • Gosselet Pierre
  • Rixen Daniel
  • Spillane Nicole
  • Roux François-Xavier
  , 2015. no abstract
• Coupling techniques for nonlinear hyperbolic equations. IV. Well-balanced schemes for scalar multi-dimensional and multi-component laws
  
  • Boutin Benjamin
  • Coquel Frédéric
  • LeFloch Philippe G.
  Mathematics of Computation, American Mathematical Society, 2015, 84 (294), pp.1663-1702. This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of partial differential equations. In an earlier work, this strategy allowed us to develop a regularization method based on a thick interface model in one space variable for coupling scalar equations. In the present paper, we significantly extend this framework and, in addition, encompass equations in several space variables. This new formulation includes the coupling of several distinct scalar conservation laws and allows for a possible covering in space. Our main contributions are, on one hand, the design and analysis of a well–balanced finite volume method on general triangulations and, on the other hand, a proof of convergence of this method toward entropy solutions, extending Coquel, Cockburn, and LeFloch's theory (restricted to a single conservation law without coupling). The core of our analysis is, first, the derivation of entropy inequalities as well as a discrete entropy dissipation estimate and, second, a proof of convergence toward the entropy solution of the coupling problem. (10.1090/S0025-5718-2015-02933-0)
  DOI : 10.1090/S0025-5718-2015-02933-0
• Developmental Partial Differential Equations
  
  • Pouradier Duteil Nastassia
  • Rossi Francesco
  • Boscain Ugo
  • Piccoli Benedetto
  , 2015. In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold’s evolution. In other words, the manifold’s evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold’s geometry. DPDE is used to study a diffusion equation with source on a growing surface whose growth depends on the intensity of the diffused quantity. The surface may, for instance, represent the membrane of an egg chamber and the diffused quantity a protein activating a signaling pathway leading to growth. Our main objective is to show controllability of the surface shape using a fixed source with variable intensity for the diffusion. More specifically, we look for a control driving a symmetric manifold shape to any other symmetric shape in a given time interval. For the diffusion we take directly the Laplace-Beltrami operator of the surface, while the surface growth is assumed to be equal to the value of the diffused quantity. We introduce a theoretical framework, provide approximate controllability and show numerical results. Future applications include a specific model for the oogenesis of Drosophila melanogaster.