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2019 Thermal avalanche after non-simultaneous blow-up in heat equations coupled via nonlinear boundary
Bingchen Liu, Fengjie Li, Mengzhen Dong
Rocky Mountain J. Math. 49(3): 817-847 (2019). DOI: 10.1216/RMJ-2019-49-3-817

Abstract

In this paper, we study a parabolic problem defined in the half line coupled via exponential-type boundary flux. Firstly, we prove the optimal classification of the two components of blow-up solutions when time reaches the blow-up time from left. Blow-up takes place only at the origin, and simultaneous blow-up rates are determined as well. Secondly, we study the weak extension after the blow-up time. Complete blow-up always occurs whether simultaneous blow-up arises or not. Moreover, an instantaneous propagation of the blow-up singularity to the whole spatial domain occurs at the blow-up time, which is the so-called thermal avalanche phenomenon. Finally, we use the evolution of the $k$-level set of solutions in the approximations to characterize the propagation of the singularity.

Citation

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Bingchen Liu. Fengjie Li. Mengzhen Dong. "Thermal avalanche after non-simultaneous blow-up in heat equations coupled via nonlinear boundary." Rocky Mountain J. Math. 49 (3) 817 - 847, 2019. https://doi.org/10.1216/RMJ-2019-49-3-817

Information

Published: 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07088338
MathSciNet: MR3983302
Digital Object Identifier: 10.1216/RMJ-2019-49-3-817

Subjects:
Primary: 35B60, 35K57, 35K60

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 3 • 2019
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