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

Document Type : Original Article

Authors

1 Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam

2 Division of Applied Mathematics, Science and Technology Advanced Institute Van Lang University, Ho Chi Minh City, Viet Nam

3 Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, Vietnam

Abstract

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 $L^{r}(0,\pi)$. We obtain an approximated solution using the Fourier method and the final input data $L^{r}(0,\pi)$ for $r \neq 2$. Using embedding between $L^{r}(0,\pi)$ and Hilbert scales $\mathcal{H}^{\rho}(0,\pi)$, this study is the error between the exact and regularized solutions to be estimated in $L^{r}(0,\pi)$.

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