Inverse source problems for time-fractional nonlinear pseudoparabolic equations with p-Laplacian

Abstract

In this paper, we deal with a time dependent inverse source problem for a nonlinear p-Laplacian pseudoparabolic equation containing a fractional derivative in time of order \(\alpha \in (0,1)\). Moreover, the equation is perturbed by a power-law damping (reaction) term, which, depending on whether its sign is positive or negative, may account for the presence of a source or an absorption within the system. The equation is supplemented with a measurement in a form of an integral over space domain along with the initial and Dirichlet boundary conditions, to determine both the solution of the equation and the unknown source term. For the associated inverse source problem, under suitable assumptions on the data, we establish global and local in time existence and uniqueness of weak solutions for different values of exponents and coefficients.