Quasi-solution approach for a two dimensional nonlinear inverse diffusion problem

Abstract

This paper is related to a class of inverse problems for identification of the coefficient in a square porous medium. The unknown coefficient depends on the solution and belongs the class of admissible coefficients. Using continuous dependence of solutions on the coefficient convergence in the corresponding direct problems, the existence of the quasi-solution of the inverse problem is obtained in the appropriate class of admissible coefficients.