Uniqueness in the Cauchy problem for the heat equation

被引：17
|
作者：
Chung, SY [1 ]
机构：
[1] Sogang Univ, Dept Math, Seoul 121742, South Korea
来源：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 1999年 / 42卷
关键词：
D O I：
10.1017/S0013091500020459
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We relax the growth condition in time for uniqueness of solutions of the Cauchy problem for the heat equation as follows: Let u(x,t) be a continuous function on R-n x [0, T] satisfying the heat equation in R-n x (0, t) and the following: (i) There exist constants a > 0, 0 < alpha < 1, and C > 0 such that \u(x, t)\ less than or equal to C exp[(a/t)(z) + a\x\(2)] in R-n x (0, T). (ii) u(x, 0) = 0 for x is an element of R-n. Then u(x, t) = 0 on R-n x [0, T]. We also prove that the condition 0 < alpha < 1 is optimal.
引用
收藏
页码：455 / 468
页数：14
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