Extinction and propagation phenomena for semilinear parabolic equations on metric trees

2025/05/15 by Punzo, Fabio, Tesei, Alberto · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.10712

Abstract

We study the Cauchy-Neumann problem on a regular metric tree T for the semilinear heat equation with forcing term of KPP type. Propagation and extinction of solutions, as well as asymptotical speed of propagation are investigated.

Citations

• Monotonicity results for semilinear parabolic equations on metric graphs
• Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdős-Réyni graphs
• Heat kernels of metric trees and applications
• Population persistence under advection-diffusion in river networks
• Heat kernel estimates and related inequalities on metric graphs
• Note on basic features of large time behaviour of heat kernels
• Laplace and Schrödinger operators on regular metric trees: the discrete spectrum case
• Multidimensional nonlinear diffusion arising in population genetics

Cited by

• Nonexistence results for the semilinear wave equation on graphs

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