On the uniqueness for the heat equation with density on infinite graphs

2024/09/05 by Meglioli, Giulia · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.03617

Abstract

We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bounded from below by a positive constant and the case of possibly vanishing density, showing that these two scenarios lead to two different classes of uniqueness.

Cited by

• Blow up results and lifespan estimates for nonlinear damped wave equations on weighted graphs
• Rigidity for the heat equation with density on Riemannian manifolds through a conformal change

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