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Acta Mathematica Vietnamica

REGULARIZATION OF A BACKWARD HEAT TRANSFER PROBLEM WITH A NONLINEAR SOURCE

DANG DUC TRONG, NGUYEN MINH DIEN

Abstract

We consider the problem of finding, from the final data u(x,T), the function u satisfying utuxx=f(x,t,u(x,t),ux(x,t)),(x,t)R×(0,T). The problem is ill-posed and we shall use the Fourier transform to get a nonlinear integral equation in the frequency space. By truncating high frequencies, we give a regularized solution. Error estimates are given.