BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

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BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

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doi:10.1007/s10473-024-0213-0

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (2): 609-631.doi: 10.1007/s10473-024-0213-0

Yiting WU

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

收稿日期:2022-06-30 修回日期:2023-10-16 出版日期:2024-04-25 发布日期:2024-04-16
作者简介:Yiting WU, E-mail: yitingwu@cjlu.edu.cn; yitingly@126.com
基金资助:
Zhejiang Provincial Natural Science Foundation of China (LY21A010016) and the National Natural Science Foundation of China (11901550).

Yiting WU

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

Received:2022-06-30 Revised:2023-10-16 Online:2024-04-25 Published:2024-04-16
About author:Yiting WU, E-mail: yitingwu@cjlu.edu.cn; yitingly@126.com
Supported by:
Zhejiang Provincial Natural Science Foundation of China (LY21A010016) and the National Natural Science Foundation of China (11901550).

摘要： 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).

关键词: semilinear parabolic system on graphs, blow-up, heat kernel estimate on graphs

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).

Key words: semilinear parabolic system on graphs, blow-up, heat kernel estimate on graphs

中图分类号:

35R02

Yiting WU. BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS[J]. 数学物理学报(英文版), 2024, 44(2): 609-631.

Yiting WU. BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS[J]. Acta mathematica scientia,Series B, 2024, 44(2): 609-631.

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