arXiv subjects

Hector Bouton

Publications and source records attributed to Hector Bouton.

5 recordsLinked to original sources

arXiv2026

Simple proofs for the existence of smooth solutions to a reaction-diffusion system modeling reversible chemistry

We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions $d\leq 3$ of the system of reaction diffusion $ \partial\_t a\_i - d\_i \Delta a\_i = (-1)^i (a\_1 a\_3 - a\_2 a\_4)$, where $a\_i \geq 0$ model the concentrations of chemical species undergoing a chemical reaction and diffusing (each with its diffusion rate $d\_i > 0$) in a bounded container.

math.AP↗

arXiv2026

Improved convergence rates in the fast-reaction approximation of the triangular Shigesada-Kawasaki-Teramoto system

We consider the fast-reaction approximation to the triangular Shigesada-Kawasaki-Teramoto model on a bounded domain in the physical dimension $d\le 3$. We provide explicit convergence rates on the whole domain in $\textnormal{L}^\infty\textnormal{L}^2\cap\textnormal{L}^2\textnormal{H}^1$ and in the interior we prove convergence with an explicit rate in any $\textnormal{L}^\infty\textnormal{H}^l$ for all $l > 0$.

math.AP↗

arXiv2025

H{\"o}lder regularity of parabolic equations with Dirichlet boundary conditions and application to reaction-diffusion and reaction-cross-diffusion systems

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 $a\partial_t w - \Delta w = f$ with a rough coefficient $a$, homogeneous Dirichlet boundary conditions, and the special assumption $\partial_tw \ge 0$. We then apply it to prove existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lotka-Volterra reaction terms in three dimensions and Dirichlet boundary conditions, and to obtain estimates for solutions to reaction-diffusion systems modeling reversible chemistry (still when Dirichlet boundary conditions are considered).

math.AP↗

arXiv2025

Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions

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. A key part is the independent careful study of the parabolic equation $a\partial_t w - \Delta w = f$ with a rough coefficient $a$, homogeneous Neumann boundary conditions, and the special assumption $\partial_t w \ge 0$. By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry.

math.AP↗

arXiv2025

Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions

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. A key part is the independent careful study of the parabolic equation $a\partial_t w - \Delta w = f$ with a rough coefficient $a$, homogeneous Neumann boundary conditions, and the special assumption $\partial_tw \ge 0$. By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry.

math.AP↗