一类抛物型方程不适定问题的解法

近年来,人们发现数学物理中许多不适定问题具有重大的应用价值。本文研究了一类抛物型方程不适定问题的解法,找到了稳定近似解的分析表达式。我们的方法克服了拟逆法在稳定性方面遇到的困难,而且我们的方法也能适用于某类线性算子方程中。

The Solution of an I11 - posed Problem for a Class of Parabolic Equations

I n this paper, We investigate an ill - posed problem for parabolic equations of the from Where G is a bounded open set in Rn with Smooth boundary G. We assume that. In case f(x) G H01(G), a stable approximate solution in H01(G) of (1) is obtained by applying the A, N, Tikhonov's regularization method and by choosing a well - posed problem (See theorems 1 and 2). Our method is different form the Qua-sireversibility method, the latter method is not so good for some class of linear operater equations.