Quenching for a parabolic system with general singular terms

Volume 9, Issue 8, pp 5281--5290 http://dx.doi.org/10.22436/jnsa.009.08.14

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Authors

Haijie Pei - College of Mathematics and Information, China West Normal University, Nanchong 637009, P. R. China. Zhongping Li - College of Mathematics and Information, China West Normal University, Nanchong 637009, P. R. China.

Abstract

In this paper, we study a parabolic system with general singular terms and positive Dirichlet boundary conditions. Some sufficient conditions for finite-time quenching and global existence of the solutions are obtained, and the blow-up of time-derivatives at the quenching point is verified. Furthermore, under some appropriate hypotheses, we prove that the quenching point is only origin and quenching of the system is non-simultaneous. Moreover, the estimate of quenching rate of the corresponding solution is established in this article.

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Keywords

• Quenching
• quenching set
• quenching rate
• singular term
• parabolic system.

MSC

•  35K51
•  35K61
•  35B44

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