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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 8
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Articles

Blow-up for the ω-heat equation with Dirichlet boundary conditions and a reaction term on graphs

, &
Pages 1691-1701 | Received 28 Jun 2013, Accepted 04 Sep 2013, Published online: 07 Oct 2013
 

Abstract

In this paper, we consider the blow-up phenomenon for the -heat equation on graph with Dirichlet boundary conditions and a reaction termwhere is called the discrete weighted Laplacian operators. If , every solution is global, and if and under some suitable conditions, we prove that the nonnegative and nontrivial solution blows up in finite time and the blow-up rate on -norm only depends on p. Finally, two examples are proposed to demonstrate our results.

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Acknowledgements

We want to thank the referees for their comments, which helped us to improve this manuscript.

Notes

This paper is supported in part by NSF of China [grant number 11226190] and in part by the Fund of the Key Disciplines in the General Colleges and Universities of Xin Jiang Uygur Autonomous Region [grant number 2012ZDXK08].

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