Life span of solutions to a semilinear parabolic equation on locally finite graphs

2024/05/28 by Yuanyang Hu, Mingxin Wang, Hu, Yuanyang +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2405.18173

openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G=(V,E) be a locally finite connected graph. We develop the first eigenvalue method on G introduced in 1963 by Kaplan \citeKaplan on Euclidean space, the discrete Phragmén-Lindelöf principle of parabolic equations and upper and lower solutions method on G. Using these methods, we establish the estimates and asymptotic behaviour of the life span of solutions to a semilinear heat equation with initial data λψ(x) for different scales of λ on G under some different conditions. Our results are different from the continuous case, which is related to the structure of the graph G.

Related

• The lifespan of positive solutions of heat equation with power-logarithmic nonlinearity on locally finite graph
• Blow-up and global existence for semilinear parabolic equations on infinite graphs
• L^p-L^q estimates of the heat kernels on graphs with applications to a parabolic system
• Semilinear heat equations and parabolic variational inequalities on graphs
• On a semilinear parabolic equation with time-dependent source term on infinite graphs