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arXiv · 2502.13150

On a semilinear parabolic equation with time-dependent source term on infinite graphs

Fabio Punzo·Alessandro Sacco
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Abstract

We are concerned with semilinear parabolic equations, with a time-dependent source term of the form $h(t)u^q$ with $q>1$, posed on an infinite graph. We assume that the bottom of the $L^2$-spectrum of the Laplacian on the graph, denoted by $\lambda_1(G)$, is positive. In dependence of $q, h(t)$ and $\lambda_1(G)$, we show global in time existence or finite time blow-up of solutions.

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Fabio Punzo, Alessandro Sacco. 2025-02-12. On a semilinear parabolic equation with time-dependent source term on infinite graphs. https://arxiv.org/abs/2502.13150

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