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This paper studies a longitudinal shape transformation model in which shapesare deformed in response to an internal growth potential that evolves accordingto an advection reaction diffusion process. This model extends prior works thatconsidered a static growth potential, i.e., the initial growth potential isonly advected by diffeomorphisms. We focus on the mathematical study of thecorresponding system of coupled PDEs describing the joint dynamics of thediffeomorphic transformation together with the growth potential on the movingdomain. Specifically, we prove the uniqueness and long time existence ofsolutions to this system with reasonable initial and boundary conditions aswell as regularization on deformation fields. In addition, we provide a fewsimple simulations of this model in the case of isotropic elastic materials in2D.

Diffeomorphic shape evolution coupled with a reaction-diffusion PDE on a growth potential