Mathematical analysis/Partial differential equations
The quenching behavior of a quasilinear parabolic equation with double singular sources
Comptes Rendus. Mathématique, Volume 356 (2018) no. 7, pp. 725-731.

In this paper, we study the quenching behavior for a one-dimensional quasilinear parabolic equation with singular reaction term and singular boundary flux. Under certain conditions on the initial data, we show that quenching occurs only on the boundary in finite time. Moreover, we derive some lower and upper bounds of the quenching rate and get some estimates for the quenching time.

Nous étudions ici le comportement désactivant d'une équation parabolique quasi-linéaire avec un terme de réaction singulier et un flux au bord singulier. Sous certaines conditions sur les données initiales, nous montrons que la désactivation intervient seulement au bord en temps fini. De plus, nous obtenons des bornes inférieure et supérieure du taux de désactivation ainsi que des estimations du temps de désactivation.

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DOI: 10.1016/j.crma.2018.05.013
Zhu, Liping 1

1 College of Science, Xi'an University of Architecture & Technology, Xi'an, 710055, China
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Zhu, Liping. The quenching behavior of a quasilinear parabolic equation with double singular sources. Comptes Rendus. Mathématique, Volume 356 (2018) no. 7, pp. 725-731. doi : 10.1016/j.crma.2018.05.013. http://www.numdam.org/articles/10.1016/j.crma.2018.05.013/

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