ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF THE CAUCHY PROBLEM FOR NONLINEAR PARABOLIC EQUATIONS

被引：10

作者：

Ishige, Kazuhiro ^{[1
]}

Kawakami, Tatsuki ^{[2
]}

机构：

[1] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

[2] Osaka Prefecture Univ, Dept Math Sci, Sakai, Osaka 5998531, Japan

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2013年 / 121卷

关键词：

LARGE TIME BEHAVIOR; CONVECTION-DIFFUSION EQUATIONS; HEAT-EQUATION; CHEMOTAXIS; SYSTEM; DECAY; PROFILES;

D O I：

10.1007/s11854-013-0038-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the Cauchy problem for the nonlinear parabolic equation tu = 1 u + F(x, t, u,. u) in R N x (0,8), u(x, 0) =.(x) in R N, where N = 1, F. C(R N x (0,8) x R x R N),.. L 8(R N) n L 1 (R N, (1 + | x| K) dx) for some K >= 0. We give a sufficient condition for the solution to behave like a multiple of the Gauss kernel as t -> a and obtain the higher order asymptotic expansions of the solution in W (1,q) (R (N) ) with 1 a parts per thousand currency sign q a parts per thousand currency sign a infinity.

引用

页码：317 / 351

页数：35

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