一类求解抛物型方程侧边值问题的最优滤波方法

Abstract

Abstract:

The authors consider a sideways parabolic equation in the quarter plane, i.e., a non-standard inverse heat conduction equation with convection term. People want determine the solution u(x, t) for 0 < x <1 from the data along the line x=1. This is an ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. Some special regularization method is needed for solving this problem. This paper considers an optimal filtering method and gives the H\"{o}lder optimal error estimate between the exact
solution and its regularized approximation solution. Furthermore, the convergence of the regularized approximation solution at x=0 is also obtained.

Key words: Ill-posed problem, Sideways parabolic equation, Optimal filter , method, Error estimate

CLC Number:

35R25

LI Hong-Fang, FU Chu-Li, XIONG Xiang-Qiu, NA Nan. An Optimal Filtering Method for Solving a |Sideways Parabolic Equation[J].Acta mathematica scientia,Series A, 2009, 29(2): 245-252.

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An Optimal Filtering Method for Solving a |Sideways Parabolic Equation

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