Hector Bouton

collaborators

7 papers

math.AP2026

Upper and lower bounds for heat kernels with very strong degeneracy

Hector Bouton

We consider the following degenerate parabolic equation on a bounded domain of $R^{d}$ containing $0$ : $\partial_{t} u - \nabla \cdot (φ (t, x) \nabla u) = 0$ , where $φ$ is a roug…

math.AP2026

Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension

Hector Bouton

We consider a discrete coagulation-fragmentation-diffusion system on a bounded domain of $R^{d}$ . In dimension $d \leq 2$ , we prove mass conservation (that is absence of gela…

math.AP2026

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 $d \leq 3$ of the system of reaction diffusion $ \partial\_t a\_i - d\_i Δa\_i…

math.AP2026

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

Hector Bouton

We consider the fast-reaction approximation to the triangular Shigesada-Kawasaki-Teramoto model on a bounded domain in the physical dimension $d \leq 3$ . We provide explicit converge…

math.AP2025

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 $a \partial_{t} w - Δ w = f$ with a…

math.AP2025

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.…

math.AP2025

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.…