Year: 2026
Type: article
Abstract: We investigate quasilinear discrete PDEs ∂ t u = Δ N φ ( u ) + K f ( u ) \partial _t u = \Delta ^N \varphi (u)+ Kf(u) of reaction-diffusion type with nonlinear diffusion term defined on an n n -dimensional unit torus discretized with mesh size 1 N \tfrac 1N for N ∈ N N\in {\mathbb {N}} , where Δ N \Delta ^N is the normalized discrete Laplacian, φ \varphi is a strictly increasing C 5 C^5 function and f f is a C 1 C^1 function. We establish L ∞ L^\infty bounds and space-time Hölder estimates, both uniform in N N , of the first and second spatial discrete derivatives of the solutions. In the equation, K > 0 K>0 is a large constant and we show how these estimates depend on K K
DOI: 10.1090/memo/1612
Authors: Tadahisa Funaki, Sunder Sethuraman
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7127620168