Identifying of unknown source term for the Rayleigh-Stokes problem

Abstract

In this paper, we would like to briefly introduce some applications of fractional derivatives in the fields of heat and fluid-flows. However, our main focus is on study an inverse source problem for the Rayleigh-Stokes problem. The problem is severely ill-posed. We verify the ill-posedness of Problem 1, applying the modified Lavrentiev to construct a regularization from the exact data. After that, we established the convergent rate between the exact solution and its approximation. Furthermore, we have the estimate in Lq space.