APPROXIMATION OF A PARABOLIC NONLINEAR EVOLUTION EQUATION BACKWARDS IN TIME

被引：27

作者：

LONG, NT ^{[1
]}

DINH, APN ^{[1
]}

机构：

[1] UNIV ORLEANS,MATH APPL & PHYS MATH LAB,URA 1803,F-45067 ORLEANS 2,FRANCE

来源：

INVERSE PROBLEMS | 1994年 / 10卷 / 04期

关键词：

D O I：

10.1088/0266-5611/10/4/010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the inverse time problem for the non-linear heat equation in the form u(t) + Au = f(u), u(1) = X, where A is any non-negative. self adjoint operator. Using the strongly continuous contraction semi-group generated by A(beta) = -A(I + betaA)-1, beta > 0, we derive an estimation of the error on the whole interval (0,1] between u(t), solution of the initial problem, and upsilon(beta)(t), solution of the regularized problem: upsilon(beta)(t) + A(beta)upsilon3(t) = e-(1-t)betaAAbeta.f(upsilon(beta)), upsilon(beta)(1) = X.

引用

页码：905 / 914

页数：10