arXiv subjects

Kenichi Fujishiro

Publications and source records attributed to Kenichi Fujishiro.

4 recordsLinked to original sources

arXiv2018

An inverse problem for distributed order time-fractional diffusion equations

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.

math.AP↗

arXiv2015

Determination of time dependent factors of coefficients in fractional diffusion equations

We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in a bounded domain.

math.AP↗

arXiv2015

Non-homogeneous boundary value problems for fractional diffusion equations in $L^2$-setting

In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet boundary data. The main tool we use here is called the transposition method.

math.AP↗

arXiv2015

Approximate controllability for fractional diffusion equations by Dirichlet boundary control

In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary conditions using the eigenfunction expansion. Next we also study the dual system and apply their results to prove (i) the regularity of the solution with non-smooth boundary conditions and (ii) approximate controllability.

math.OC↗