A finite time extinction profile and optimal decay for a fast diffusive doubly nonlinear equation

被引：0
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作者：
Masashi Misawa
Kenta Nakamura
Md Abu Hanif Sarkar
机构：
[1] Kumamoto University,Faculty of Advanced Science and Technology
[2] Kumamoto University,Headquarters for Admissions and Education
[3] Kumamoto University,undefined
来源：
Nonlinear Differential Equations and Applications NoDEA | 2023年 / 30卷
关键词：
Complete extinction; Finite time extinction; Expansion of positivity; Regularity; Nonlinear intrinsic scaling transformation; Primary: 35B45; 35B65; Secondary: 35D30; 35K61;
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摘要：
In this article, we consider a fast diffusive type doubly nonlinear parabolic equation and study the extinction behavior of a solution at a finite time. We show the complete extinction of a weak solution with a nonnegative initial datum, that is, a weak solution is positive before a finite time and vanishes after it, and derive the optimal decay estimates of extinction. Our key ingredient of the proof is a nonlinear intrinsic scaling and the expansion of positivity.
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