Several Studies Parabolic Equations Of Inverse Problems

Due to the need for practical problems, more and more people put attentionto inverse problem of mathematical physics. In this paper, we investigate two kindsof inverse parabolic diferential equations: backward heat conduction problem andinverse source heat conduction problem. Both of them are severe ill-posed problem,we must be use proper method to solve them.In this paper, frstly, logarithmic convexity method is utilized for consideringa one-dimensional backward heat conduction problem, we obtain its conditionalstability estimate, error estimation of between exact solution and regular solution;Then, we use Fourier truncation regularization method to study a two-dimensionalinverse source heat conduction problem, and receive Fourier regular solution, errorestimation of between exact solution and regular solution. Numberical examples aregiven which show the efciency of our methods.