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An Inverse Source Problem in a Variable-Order Time-Fractional Diffusion PDE
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DOI：10.3390/math14030488.png)
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Abstract
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We study an inverse source problem for a semilinear diffusion equation involving a Caputo-type time-fractional derivative whose order is a function of time. The equation is considered in a bounded Lipschitz domain Omega subset of Rd, d >= 1, and is supplemented with homogeneous Dirichlet boundary conditions. The source term is taken to be separable, h(t)f(x), where the temporal component h(t) is unknown. This quantity is to be identified from spatially localized measurements m(t) of the solution. In this setting, we establish existence and uniqueness results in suitable function spaces, thereby demonstrating the well-posedness of the corresponding inverse source problem.
Keywords:
inverse source problem
nonlinear time-fractional diffusion equation
variable order
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