Refined asymptotic profiles for a semilinear heat equation
Refined asymptotic profiles for a semilinear heat equation
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DOI：
10.1007/s00208-011-0677-9
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发表时间：
2012-05
影响因子：
1.4
通讯作者：
Kazuhiro Ishige;Tatsuki Kawakami
中科院分区：
文献类型：
--
作者：
Kazuhiro Ishige;Tatsuki Kawakami
研究了一类半线性热方程Cauchy问题解的长时间行为，其中K≥ 0。设u是（P）的一个解，对某些常数C > 0和A > 1，满足.那么众所周知，解u的行为就像热核。本文给出了解u的（[K]+2）阶渐近展开式，并揭示了解u的渐近轮廓与非线性项F之间的关系。这里[K]是满足K− 1 <[K]≤ K的整数。
We study the large time behavior of the solutions of the Cauchy problem for a semilinear heat equation, whereandwith K≥ 0. Assume that u is a solution of (P) satisfying for some constants C > 0 and A > 1. Then it is well known that the solution u behaves like the heat kernel. In this paper we give the ([K]+ 2) th order asymptotic expansion of the solution u, and reveal the relationship between the asymptotic profile of the solution u and the nonlinear term F. Here [K] is the integer satisfying K− 1 <[K]≤ K.