A Quasi Solution for a Nonlinear Inverse Stochastic Partial Differential Equation of Parabolic Type

This paper concerns a nonlinear inverse stochastic parabolic partial differential equation. The source term of this problem consists branches of science and engineering, of known multiplicative noise. We study the existence of the quasi solution for this problem. Our suggested method to this approach is the minimization method based on the stochastic variational formulation. Moreover, we prove a stability estimation and continuity of minimization functional. In the proof procedure, we show that there is a compact subset of the admissible functions set. These results prove the existence of a quasi solution for the proposed problem.