Blow-up conditions for a semilinear parabolic system on locally finite graphs

DOI10.1007/s10473-024-0213-0OpenAlexW4391568301WikidataQ128466208 ScholiaQ128466208MaRDI QIDQ6192417

Yiting Wu

Publication date: 11 March 2024

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10473-024-0213-0

zbMATH Keywords

blow-upheat kernel estimate on graphssemilinear parabolic system on graphs

Mathematics Subject Classification ID

Blow-up in context of PDEs (35B44) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91) Heat kernel (35K08) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Cites Work

• On uniqueness class for a heat equation on graphs
• Time regularity and long-time behavior of parabolic \(p\)-Laplace equations on infinite graphs
• Kazdan-Warner equation on graph
• Analysis of the physical Laplacian and the heat flow on a locally finite graph
• Boundedness and blow up for a semilinear reaction-diffusion system
• A semilinear parabolic system in a bounded domain
• Liouville theorems and blow up behaviour in semilinear reaction diffusion systems
• Existence of positive solutions to some nonlinear equations on locally finite graphs
• Convergence of ground state solutions for nonlinear Schrödinger equations on graphs
• A heat flow for the mean field equation on a finite graph
• Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs
• Blow-up for a semilinear heat equation with Fujita's critical exponent on locally finite graphs
• Multiple solutions of Kazdan-Warner equation on graphs in the negative case
• The existence of extremal functions for discrete Sobolev inequalities on lattice graphs
• Blow-up problems for nonlinear parabolic equations on locally finite graphs
• The existence and nonexistence of global solutions for a semilinear heat equation on graphs
• Kazdan-Warner equation on graph in the negative case
• Dirichlet forms and stochastic completeness of graphs and subgraphs
• A note on Liouville type equations on graphs
• Application of Rothe's method to a nonlinear wave equation on graphs
• The pth Kazdan–Warner equation on graphs
• Heat kernel and essential spectrum of infinite graphs

This page was built for publication: Blow-up conditions for a semilinear parabolic system on locally finite graphs