A BACKWARD PROBLEM FOR THE NONLINEAR DIFFUSION EQUATION WITH COUPLING OPERATOR OF LOCAL AND NONLOCAL TYPE AND GAUSSIAN WHITE NOISE ON THE MEASUREMENT

Abstract

In this paper, we consider the problem of recovering the heat distribution for anonlinear diffusion equation with local and nonlocal operators with Gaussian white noise. As commonly acknowledged, the problem is severely ill-posed according to Hadamard's definition.Consequently, we propose the Fourier truncation method to regularize the problem.With different assumptions on the exact solution, the estimation of the expectation of the error between the regularized solution and the exact solution is obtained.