Deux méthodes de régularisation pour un problème inverse de conduction thermique semi-linéaire mal-posé

Abstract

ii Abstract The present memory we consider an inverse semi linear heat conduction problem, and we assume that there existe a heat source which is significantly dependant on space, time and temperature and heat flux. The problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the cauchy data. In order to obtain a stable numerical solution, we propose two regularization methods to solve the semilinear problem in which the heat source is a Lipschitz function of temperature. we show rigourously, with error estimates provided, that the corresponding regularized solutions converge to the true solution strongly in L2 uniformily with respect to the space coordinate under some a priori assumptions on the solution