Extinction and propagation phenomena for semilinear parabolic equations on metric trees

Alberto Tesei; Fabio Punzo

Extinction and propagation phenomena for semilinear parabolic equations on metric trees

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arxiv 2505.10712 v1 pith:BJ2ORZCZ submitted 2025-05-15 math.AP

Fabio Punzo , Alberto Tesei This is my paper · ORCID

classification math.AP

keywords propagationextinctionmetricsemilinearasymptoticalcauchy-neumannequationequations

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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.

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Nonexistence results for the semilinear wave equation on graphs
math.AP 2025-06 reject novelty 6.0 of 10

On infinite weighted graphs, if the graph Laplacian of the distance grows slowly and suitable weighted volume growth holds, every very weak solution of the semilinear wave inequality is identically zero.

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