Résumé:
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
