Behavior of blow-up solutions for quasilinear parabolic equations

被引：0

作者：

Yevgenieva Y.A. ^{[1
]}

机构：

[1] Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slov’yans’k

来源：

Journal of Mathematical Sciences | 2020年 / 249卷 / 5期

关键词：

method of energy estimates; Quasilinear parabolic equation; singular boundary data; weak solution;

D O I：

10.1007/s10958-020-04974-z

中图分类号：

学科分类号：

摘要：

We study the quasilinear parabolic equation (|u|q − 1u)t − Δpu = 0 in a multidimensional domain (0, T) × Ω under the condition u(t; x) = f(t,x) on (0,T) × əΩ, where the boundary function f blows-up at a finite time T, i.e., f(t; x) → ∞ as t → T. For p q > 0 and the boundary function f with power-like behavior, the upper bounds of weak solutions of the problem are obtained. The behavior of solutions at the transition from the case where p > q to p = q is investigated. A general approach within the method of energy estimates to such problems is described. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：804 / 816

页数：12

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