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arXiv · 2004.07596

Blow-up for a semilinear heat equation with Fujita's critical exponent on locally finite graphs

Yiting Wu
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Abstract

Let $G=(V,E)$ be a locally finite, connected and weighted graph. We prove that, for a graph satisfying curvature dimension condition $CDE'(n,0)$ and uniform polynomial volume growth of degree $m$, all non-negative solutions of the equation $\partial_tu=Δu+u^{1+α}$ blow up in a finite time provided that $α=\frac{2}{m}$. We also consider the blow-up problem under certain conditions for volume growth and initial value. The obtained results provide a significant complement to the work by Lin and Wu in earlier paper.

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Yiting Wu. 2020-04-16. Blow-up for a semilinear heat equation with Fujita's critical exponent on locally finite graphs. https://arxiv.org/abs/2004.07596

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