| 研究実績の概要 |
The anomalous diffusion processes were found in many problems in the fields of science and engineering. For the qualitative analysis of these problem, a macro-model named time-fractional diffusion equation with Caputo derivative is derived by using the continuous time random walk. We considered two kinds of inverse problem:
1. Unique continuation. By using Theta function method and Laplace transform argument, we proved a classical type unique continuation, say, the vanishment of a solution to a the fractional diffusion equation in an open subset implies its vanishment in the whole domain provided the solution vanishes on the whole boundary.
2. Inverse problem in determining the fractional order. By exploiting the integral equation of the solution u to the our problem, and carrying out the inversion Laplace transforms, we verified the Lipschitz continuous dependency of the fractional order with respect to the overposed data.
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