7 papers · 1 filter
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 containing : , where is a roug…
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 . In dimension , we prove mass conservation (that is absence of gela…
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 Δa\_i…
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 . We provide explicit converge…
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 a…
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.…