摘要
在反问题的研究中,确定未知系数的问题和确定未知边界的问题(自由边界问题)通常是分开进行研究的。本文将这两者结合起来,对非线性热传导方程:a(u)ut=k(a(u)ux)x,(0<x<s(t),0<t ≤T),证明了解{a(u),s(t),u(x,t)}是存在的、唯一的并且是稳定的。
The problem of determining unknown coefficients and unknown boundaries (or free boundary problem) is usually studied partly in the research of inverse problems. This paper, combining the two problems, deals with the nonlinear heat conduction equation a (u)u_t= k(a(u)u_x)_x(0 <x <s(t), 0<t ≤T) and proves the existence, stability and uniqueness of the solution {a(u), s(t), u(x, t)}.
出处
《哈尔滨商业大学学报(自然科学版)》
CAS
1999年第1期50-55,58,共7页
Journal of Harbin University of Commerce:Natural Sciences Edition
基金
哈尔滨工业大学基金
关键词
反问题
自由边界问题
inverse problem
free boundary problem