Initial-boundary value problem for distributed order time-fractional diffusion equations

摘要

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency on initial value and source term. Moreover, we provide energy estimates of the solution for small and large times. Finally, under suitable assumption on the source term, we establish that the solution is analytic in time.