Source Identification Problem for a Nonlinear Subdiffusion Equation
Abstract
The work is devoted to the study of the inverse problem of determining the right-hand side of a nonlinear subdiffusion equation with a Caputo derivative with respect to time. Nonlinearity of the equation means that the right-hand side of the equation depends nonlinearly on the solution of the equation. The inverse problem consists of reconstructing the coefficient of the right-hand side, which depends on both time and spatial variables, under a measurement in an integral form. Similar inverse problems were previously studied in the case when the right-hand side depends only on time or on a spatial variable. A weak solution is sought by the Galerkin method. A priori estimates are proved, and with their help, the existence and uniqueness of a solution to the inverse problem under consideration are established. It is noteworthy that the results obtained are new for diffusion equations as well.
Cite
@article{arxiv.2506.11519,
title = {Source Identification Problem for a Nonlinear Subdiffusion Equation},
author = {R. R. Ashurov and O. T. Mukhiddinova},
journal= {arXiv preprint arXiv:2506.11519},
year = {2025}
}