Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations

Abstract

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be directly measured, which requires one to discuss inverse problems of identifying these physical quantities from some indirectly observed information of solutions. Inverse problems in determining these unknown parameters of the model are not only theoretically interesting, but also necessary for finding solutions to initial-boundary value problems and studying properties of solutions. This chapter surveys works on such inverse problems for fractional diffusion equations.

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• Initial-boundary value problems for coupled systems of time-fractional diffusion equations
• Stability and numerical analysis of backward problem for subdiffusion with time-dependent coefficients
• Regularized Reconstruction of Scalar Parameters in Subdiffusion with Memory via a Nonlocal Observation