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Numerical quenching of a system of equations coupled at the boundary

✍ Scribed by Raúl Ferreira; Mayte Pérez-Llanos

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
175 KB
Volume
32
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We study numerical approximations of solutions of the following system of heat equations, coupled at the boundary through a nonlinear flux:

where p and q are parameters. We prove that the solutions of a semidiscretization in space quench in finite time. Moreover, we describe in terms of p and q the simultaneous versus non‐simultaneous quenching phenomena. We also find the numerical extinction sets. Finally, in order to obtain the correct quenching rates in the non‐simultaneous case we present some adaptive methods. Copyright © 2009 John Wiley & Sons, Ltd.

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