Extinction and propagation phenomena for semilinear parabolic equations on metric trees
Fabio Punzo, Alberto Tesei
TL;DR
This paper investigates how solutions to a semilinear heat equation on metric trees either die out or spread, analyzing their long-term behavior and speed of propagation.
Contribution
It introduces new analysis of propagation and extinction phenomena for semilinear parabolic equations on metric trees, focusing on asymptotic propagation speed.
Findings
Conditions for solution extinction and propagation identified
Asymptotic speed of propagation characterized
Behavior of solutions depends on the structure of the metric tree
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Partial Differential Equations · advanced mathematical theories · Geometric Analysis and Curvature Flows