Uniqueness in the Cauchy problem for the heat equation
Uniqueness in the Cauchy problem for the heat equation
复制标题
热方程柯西问题的唯一性
DOI：
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发表时间：
1999
影响因子：
0.7
通讯作者：
Soon‐Yeong Chung
中科院分区：
文献类型：
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作者：
Soon‐Yeong Chung
我们在时间上放宽热方程Cauchy问题解的唯一性生长条件如下：设u（x, t）是一个连续函数，它在一个连续函数上满足在一个连续函数上的热方程在一个连续函数上满足：(i)存在常数a > 0, 0 < α < 1，和C >0，使得（ii） u(x, 0) = 0，对于x∈，(i) u(x, 0) = 0。则u(x, t)≡0在f (n) x [0， t]上也证明了条件0 < α < 1是最优的。
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 ℝn × [0, T] satisfying the heat equation in ℝn × (0, t) and the following: (i) There exist constants a > 0, 0 < α < 1, and C > 0 such that (ii) u(x, 0) = 0 for x ∈ ℝn. Then u(x, t)≡ 0 on ℝn × [0, T] We also prove that the condition 0 < α < 1 is optimal.