6 papers
Simple proofs for the existence of smooth solutions to a reaction-diffusion system modeling reversible chemistry
Hector Bouton, Laurent Desvillettes, Helge Dietert
We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions of the system of reaction diffusion $ \partial\_t a\_i - d\_i Îa\_i…
H{ö}lder regularity of parabolic equations with Dirichlet boundary conditions and application to reaction-diffusion and reaction-cross-diffusion systems
Hector Bouton, Laurent Desvillettes, Helge Dietert
In this work, we adapt our recent article [BDD25] to the setting of Dirichlet boundary conditions. A key part is the study of the parabolic equation with…
Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions
Hector Bouton, Laurent Desvillettes, Helge Dietert
We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions.…
Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions
Hector Bouton, Laurent Desvillettes, Helge Dietert
We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions.…
On the equilibriation of chemical reaction-diffusion systems with degenerate reactions
Laurent Desvillettes, Kim Dang Phung, Bao Quoc Tang
The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. W…
Study of a class of triangular starvation driven cross-diffusion systems
Elisabetta Brocchieri, Laurent Desvillettes, Helge Dietert
We study the existence, regularity and uniqueness for a general class of triangular reaction-cross-diffusion systems coming from the study of starvation driven behavior for two spe…