Diffeomorphic shape evolution coupled with ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Diffeomorphic shape evolution coupled with a reaction-diffusion PDE on a growth potential
Author(s) :
Hsieh, Dai-Ni [Auteur]
Arguillère, Sylvain [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Charon, Nicolas [Auteur]
Johns Hopkins University [JHU]
Younes, Laurent [Auteur]
Johns Hopkins University [JHU]
Arguillère, Sylvain [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Charon, Nicolas [Auteur]
Johns Hopkins University [JHU]
Younes, Laurent [Auteur]
Johns Hopkins University [JHU]
Journal title :
Quarterly of Applied Mathematics
Publisher :
American Mathematical Society
Publication date :
2021-08-24
ISSN :
0033-569X
HAL domain(s) :
Mathématiques [math]/Optimisation et contrôle [math.OC]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Géométrie différentielle [math.DG]
English abstract : [en]
This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends ...
Show more >This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that considered a static growth potential, i.e., the initial growth potential is only advected by diffeomorphisms. We focus on the mathematical study of the corresponding system of coupled PDEs describing the joint dynamics of the diffeomorphic transformation together with the growth potential on the moving domain. Specifically, we prove the uniqueness and long time existence of solutions to this system with reasonable initial and boundary conditions as well as regularization on deformation fields. In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D.Show less >
Show more >This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that considered a static growth potential, i.e., the initial growth potential is only advected by diffeomorphisms. We focus on the mathematical study of the corresponding system of coupled PDEs describing the joint dynamics of the diffeomorphic transformation together with the growth potential on the moving domain. Specifically, we prove the uniqueness and long time existence of solutions to this system with reasonable initial and boundary conditions as well as regularization on deformation fields. In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D.Show less >
Language :
Anglais
Popular science :
Non
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