On a Non-local Sobolev-Galpern-Type Equation Associated with Random Noise

This paper aims to retrieve the initial value for a non-local fractional Sobolev-Galpern problem. The given data are subject to noise by the discrete random model. We show that the solution to the problem is ill-posed in the sense of Hadamard. In this paper, we applied the Fourier truncation method to construct the regularized solution. We estimate the convergence between the solution and the regularized solution. In addition, the numerical example is also proposed to assess the efficiency of the theory.

Automated summary

This paper aims to retrieve the initial value for a non-local fractional Sobolev-Galpern problem. The Fourier truncation method is applied to construct the regularized solution, and the convergence between the solution and the regularized solution is estimated. Additionally, a numerical example is proposed to assess the efficiency of the theory.