Smoothing effects of the initial-boundary value problem for logarithmic type quasilinear parabolic equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Nakao, Mitsuhiro¹ 

[1] Kyushu Univ, Fac Math, Moto Oka 744, Fukuoka 8190395, Japan

关键词: Quasilinear parabolic equation;    Smoothing effects;    Moser's method;   

DOI  :  10.1016/j.jmaa.2018.02.061

来源: Elsevier

【 摘 要 】

We give existence theorems of global solutions in L-loc(infinity)((0, infinity); W-0(1,infinity)) to the initial boundary value problem for quasilinear degenerate parabolic equations of the form u(t) - div{sigma(vertical bar del u vertical bar(2))del u} = 0, where the class of sigma(v(2)) includes the logarithmic case sigma(vertical bar del u vertical bar(2)) = log (1 + vertical bar del u vertical bar(2)) for a typical example. We assume that the initial data belong to W-0(1,p0), p(0) >= 2, or L-r, r >= 1, and we derive precise estimates for parallel to del u(t)parallel to(infinity) near t = 0. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free