BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

doi:10.1016/S0252-9602(18)30788-4

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 843-856.doi: 10.1016/S0252-9602(18)30788-4

BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

林勇, 吴艺婷

Department of Mathematics, Renmin University of China, Beijing 100872, China

收稿日期:2017-04-14 修回日期:2017-07-30 出版日期:2018-06-25 发布日期:2018-06-25
通讯作者: Yiting WU E-mail:yitingly@126.com
作者简介:Yong LIN,E-mail:linyong01@ruc.edu.cn
基金资助:
The first author is supported by the National Science Foundation of China (11671401); the second author is supported by the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (17XNH106).

BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

Yong LIN, Yiting WU

Department of Mathematics, Renmin University of China, Beijing 100872, China

Received:2017-04-14 Revised:2017-07-30 Online:2018-06-25 Published:2018-06-25
Contact: Yiting WU E-mail:yitingly@126.com
Supported by:
The first author is supported by the National Science Foundation of China (11671401); the second author is supported by the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (17XNH106).

摘要/Abstract

摘要：

Let G=(V, E) be a locally finite connected weighted graph, and △ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation u_t=△u + f(u) on G. The blow-up phenomenons for u_t=△u + f(u) are discussed in terms of two cases:(i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.

关键词: Blow-up, parabolic equations, locally finite graphs, differential inequalities

Abstract:

Key words: Blow-up, parabolic equations, locally finite graphs, differential inequalities

林勇, 吴艺婷. BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS[J]. 数学物理学报(英文版), 2018, 38(3): 843-856.

Yong LIN, Yiting WU. BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS[J]. Acta mathematica scientia,Series B, 2018, 38(3): 843-856.

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BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

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