ON THE ITERATION ALGORITHM FOR AN INVERSE PROBLEM OF PARABOLIC EQUATION
一类抛物型方程系数反问题的分裂算法

Consider an inverse problem for recovering q(x) in the equation u_t-a~2u_(xx) q(x)u=0, using the final measurement data u(x,T)=Z_T(x).By introducing a function transform v=u_t/u,the solution to this nonlinear ill-posed inverse problem is obtained by two steps. We firstly solve a non-linear direct problem for v(x,t) by iteration algorithm from the inver- sion input data.This procedure is independent of the unknown coefficient q(x).Then the reconstruction of q(x) is finished from a differential relation between v and q approximately. Using this scheme,the original problem is decomposed as a nonlinear well-posed problem and an ill-posed problem.The convergence result is proven.Numerical results are given to show the validity of this decomposition scheme.