An inverse problem for distributed order time-fractional diffusion equations

Abstract

This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the distributed order time-fractional diffusion equation by means of eigenfunction expansion, which ensure that the weak solution has the classical derivatives. We next give a Harnack type inequality of the solution in the frequency domain under the Laplace transform, from which we further show a uniqueness result for an inverse problem in determining the weight function in the distributed order time derivative from point observation.

In the previous version, our result was proved provide upon Dirichlet boundary condition. Now we generalized the result to the Nuemann case

References in corpus (1)

• Approximate controllability for fractional diffusion equations by Dirichlet boundary control

Cited by in corpus (2)

• Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
• Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations