Semilinear Diffusion Equations on Infinite Graphs: The Dissipative and Lipschitz Cases
Abstract
We study a class of semilinear diffusion equations on infinite, connected, weighted graphs, focusing on two types of nonlinearities: monotone decreasing and Lipschitz continuous. Under minimal structural assumptions on the graph, we establish existence, uniqueness, and regularity of mild solutions for initial data in $\ell^p$ spaces, with $1\leq p
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Differential Equations and Boundary Problems
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 26 January 2026
- Document type
- Preprint