Inverse problems for a time fractional diffusion equation in the Schwartz-type distributions

摘要

We find the conditions for the unique solvability of the inverse problem of the solution's initial data determination for a time fractional diffusion equation with a Schwartz-type distribution in the right-hand side and the inverse problem of identifying the equation's source under given Schwartz-type distribution in the initial condition. We use a time-integral overdetermination condition.