NUMERICAL-SOLUTION OF A TIME-LIKE CAUCHY-PROBLEM FOR THE WAVE-EQUATION

被引：26

作者：

KLIBANOV, M ^{[1
]}

RAKESH ^{[1
]}

机构：

[1] UNIV DELAWARE,DEPT MATH,NEWARK,DE 19716

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 1992年 / 15卷 / 08期

关键词：

D O I：

10.1002/mma.1670150805

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let D subset-of R(n) be a bounded domain with piecewise-smooth boundary, and q(x, t) a smooth function on D x [0, T]. Consider the time-like Cauchy problem u(tt) - DELTA(x)u + q(x, t)u = 0 in D x [0, T] u = g, u(n) = h on partial derivative D x [0, T]. Given g, h for which the equation has a solution, we show how to approximate u(x, t) by solving a well posed fourth-order elliptic partial differential equation (PDE). We use the method of quasi-reversibility to construct the approximating PDE. We derive error estimates and present numerical results.

引用

页码：559 / 570

页数：12