Approximation of inverse source problem for time fractional pseudo-parabolic equation in L^p

In this work, we focus on the final value problem of an inverse problem for the pseudo-parabolic equation. This study aims to provide a regularization method for this equation, once the measurement data are obtained at the final time in L^{r}(۰,\pi). We obtain an approximated solution using the Fourier method and the final input data L^{r}(۰,\pi) for r \neq ۲. Using embedding between L^{r}(۰,\pi) and Hilbert scales \mathcal{H}^{\rho}(۰,\pi), this study is the error between the exact and regularized solutions to be estimated in L^{r}(۰,\pi).

Keywords:

Source problem , Fractional pseudo-parabolic problem , Ill-posed problem , Convergence estimates , Regularization