Regularization Methods For A Class Of Inverse Problems With Heat Source

The problems of determing unknown nonhomogeneous term are also called the prob-lems of identification unknown source. This is a typical kind of ill-posed problems. Theyare very common in our life, such as gowndwater pollution, environmental protection,heat di?usion and so on.In this paper, we study the problems of identification heat source, and consider thefollowing heat equationwhere (u, f ) is u?????n kuu?n((uox1tw,, +t0n)), u ==?x x u 0 a?(,0n ,du t xu)g (== xa , ?r 01e,() t t=)wfu o(gxx ((gx)1,i), v ,te)n (= t,f uxun)x c(∈t0i ,o( tn0),s =.1 ) 0M×, o(r0e,o 1v)e,r, we discuss thetwo-dimensional case of it. Based on the Fourier technique, we regularize it by Tikhonovmethod, Fourier method, spectral method, and molification, respectively, and considerthe essential relations of these methods.This thesis also discuss the stability of this methods, and obtain corresponding errorestimate.