摘要
考虑确定表面热流ux(0,t)的如下半无限长杆热传导方程反问题uxx=ut,0≤x,0<t,u(x,0)=0,0≤x,u(1,t)=g(t),0<t.该问题是一个严重不适定的问题,即解不连续依赖于已知数据的变化。利用磨光核函数在无穷远处的急降性质研究了反问题的条件稳定性,构造了一个适定的问题来逼近原问题,从而获得反问题的正则化解及其误差估计。数值算例表明了本文的正则化方法是有效的。
Consider the following inverse sideways heat conduction problems to determine the surface heat flux u_x(0,t):u_ xx =u_t,0≤x,0<t,u(x,0)=0,0≤x,u(1,t)=g(t),0<t.The problem is ill-posed in the sense that the solution does not depend continuously on the data.This paper discusses the conditional stability for solving the inverse sideways heat conduction problem by the rapid decreasing properties of the mollification kernel function,and obtain its regularization solution and its error estimate by constructing a well-posed problem.Moreover,numerical example shows that the regularization method is effective.
出处
《南昌大学学报（理科版）》
CAS
北大核心
2005年第3期261-265,共5页
Journal of Nanchang University(Natural Science)
基金
江西省自然科学基金资助项目(0211014)
江西省教育厅科技资助项目([2005]213)
关键词
不适定问题
热传导反问题
热流
正则化
误差估计
数值模拟
ill-posed problem
inverse heat conduction problem
heat flux
regularization
error estimate
numerical simulation
