Inverse Problems of Determining Coefficients 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, for example, the orders of the fractional derivative or the source term, are often unknown, which requires one to discuss inverse problems to identify these physical quantities from some additional information that can be observed or measured practically. This chapter investigates several kinds of inverse coefficient problems for the fractional diffusion equation.

References in corpus (4)

• On time-fractional diffusion equations with space-dependent variable order
• Recovery of a potential in a fractional diffusion equation
• Global Lipschitz stability for a fractional inverse transport problem by Carleman estimates
• Unique continuation principle for the one-dimensional time-fractional diffusion equation

Cited by in corpus (5)

• Initial-boundary value problems for coupled systems of time-fractional diffusion equations
• Inverse moving source problem for time-fractional evolution equations: Determination of profiles
• Numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation
• Stability and numerical analysis of backward problem for subdiffusion with time-dependent coefficients
• Forward and backward problems for coupled subdiffusion systems