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Blow-up conditions for a semilinear parabolic system on locally finite graphs

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Abstract

In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).

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Authors and Affiliations

  1. Department of Mathematics, China Jiliang University, Hangzhou, 310018, China

    Yiting Wu

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  1. Yiting Wu
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Correspondence to Yiting Wu.

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Conflict of Interest The author declares no conflict of interest.

Additional information

This work was partially supported by the Zhejiang Provincial Natural Science Foundation of China (LY21A010016) and the National Natural Science Foundation of China (11901550).

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Wu, Y. Blow-up conditions for a semilinear parabolic system on locally finite graphs. Acta Math Sci 44, 609–631 (2024). https://doi.org/10.1007/s10473-024-0213-0

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  • DOI: https://doi.org/10.1007/s10473-024-0213-0

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