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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 2
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Articles

Simultaneous and non-simultaneous quenching for coupled parabolic system

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Pages 233-250 | Received 09 Aug 2013, Accepted 21 Jan 2014, Published online: 28 Mar 2014
 

Abstract

In this paper, we study the quenching phenomena for a one-dimensional parabolic system coupled by non-linear boundary flux. First, we identify simultaneous and non-simultaneous quenching, then establish four kinds of simultaneous quenching rates, which are represented via the characteristic algebraic system. A precise classification of parameters is given for the multiple simultaneous quenching rates. For example, we distinguish between two kinds of subcases, with or without particular requirements on initial data, realizing a common simultaneous quenching rate. On the other hand, it is interesting to find that there are two simultaneous quenching rates which share a common subregion of parameters, determined by the initial data assumed.

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Acknowledgement

We would like to thank the referees for giving us many helpful suggestions in improving our paper.

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