Simultaneous and non-simultaneous quenching for coupled parabolic system

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.

Keywords:

• non-simultaneous quenching
• quenching rate
• characteristic algebraic system

AMS Subject Classifications:

• Primary 35K55
• 35B40
• 35K05

Acknowledgement

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