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

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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 \(\partial _tu=\Delta u+u^{1+\alpha }\) blow up in a finite time, provided that \(\alpha =\frac{2}{m}\). We also consider the blow-up problem under certain conditions for volume growth and initial value. These results complement our previous work joined with Lin.

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Acknowledgements

The work of the author is supported by the National Natural Science Foundation of China (no. 11901550), and the Natural Science Foundation of Zhejiang Province (no. LY21A010016).

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  1. Department of Mathematics, China Jiliang University, Hangzhou, 310018, People’s Republic of China

    Yiting Wu

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Wu, Y. Blow-up for a semilinear heat equation with Fujita’s critical exponent on locally finite graphs. RACSAM 115, 133 (2021). https://doi.org/10.1007/s13398-021-01075-7

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