分野別セミナー

Two inverse problems for fractional diffusion equation are investigated.
First, we proved the uniqueness of inverse source problem.
The method of eigenfunction expansion, analytic continuation and the Laplace transform
are employed. Also numerical examples are presented to illustrate the
validity and effectiveness of the proposed meshless method.
Second, we consider a special case with fractional order 1/2.
Under some regularity assumptions on
the solution and coefficient, we obtained a conditional stability
estimate of inverse coefficient problem by over-determining lateral boundary data.
The proof is based on Carleman estimates. Besides, the conditional
stability of source is another corollary.