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

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

Analysis of PDEs 2025-08-26 v2

Authors: Hector Bouton , Laurent Desvillettes , Helge Dietert

Abstract

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.

Keywords

full waveform inversion Tikhonov regularization space-variant anisotropic sparse data geological structures

Cite

@article{arxiv.2503.08186,
  title  = {Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions},
  author = {Hector Bouton and Laurent Desvillettes and Helge Dietert},
  journal= {arXiv preprint arXiv:2503.08186},
  year   = {2025}
}

Comments

32 pages; Previously this version appeared as arXiv:2507.19512 which was submitted as a new work by accident

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

Abstract

Keywords

Cite

Comments

Related papers