Stabilization of solutions to nonlinear parabolic equations of the p-Laplace type

被引：0
|
作者：
M. D. Surnachev
V. V. Zhikov
机构：
[1] Keldysh Institute of Applied Mathematics RAS,Computational Aeroacoustics Laboratory
[2] Vladimir State University,Department of Mathematics
来源：
Russian Journal of Mathematical Physics | 2013年 / 20卷
关键词：
Initial Data; Mathematical Physic; Cauchy Problem; Parabolic Equation; Nonlinear Parabolic Equation;
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摘要：
In the first part of the paper, we study the stabilization of solutions to nonlinear parabolic equations of the p-Laplace type in L2(ℝn) for 2n/(n + 2) < p ⩽ n. The proof is based on estimates uniform in time in L2(ℝn, |x|s) for p < n. For p = n, a similar estimate holds with |x|s replaced by (ln(2+|x|))s. In the second part of the paper, we prove a uniform stabilization criterion for bounded solutions. This criterion generalizes a widely known result independently proved by Zhikov and Kamin in 1976 for linear parabolic equations.
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页码：523 / 541
页数：18
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