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THE QUENCHING OF SOLUTIONS OF A REACTION–DIFFUSION EQUATION WITH FREE BOUNDARIES

Part of: Miscellaneous topics - Partial differential equations Parabolic equations and systems Partial differential equations

Published online by Cambridge University Press:  22 January 2016

NINGKUI SUN
NINGKUI SUN*
Affiliation:
Department of Mathematics, Tongji University, Shanghai 200092, China email sunnk1987@163.com
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Abstract

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This paper concerns the quenching phenomena of a reaction–diffusion equation $u_{t}=u_{xx}+1/(1-u)$ in a one dimensional varying domain $[g(t),h(t)]$, where $g(t)$ and $h(t)$ are two free boundaries evolving by a Stefan condition. We prove that all solutions will quench regardless of the choice of initial data, and we also show that the quenching set is a compact subset of the initial occupying domain and that the two free boundaries remain bounded.

Keywords

reaction–diffusion equationquenchingfree-boundary problem

MSC classification

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35R35: Free boundary problems 35B99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 110 - 120
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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