Analysis and Discrete Approximation of an Inverse Source Problem for a Time-Fractional Sobolev–Galpern Equation
Keywords:
Sobolev equation, inverse source problem, Rothe’s method, fractional derivative, uniqueness and existenceAbstract
We address an inverse source problem for a time-fractional Sobolev–Galpern-type equation endowed with Neumann boundary conditions. The goal is to reconstruct an unknown time-dependent source term from integral observations of the state variable over the spatial domain. The analysis is carried out within a variational framework, where Rothe method is employed to establish the existence and uniqueness of weak solutions under suitable assumptions on the data. A time-discrete approximation scheme is then introduced for the simultaneous computation of the state variable and the unknown source term. Rigorous convergence of the approximations is derived through energy estimates and discrete Gronwall-type arguments.
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Copyright (c) 2026 Abdeldjalil Chattouh, Djamila Chergui, Maroua Nouar
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