Affiliations: [a] Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan. E-mail: [email protected] | [b] Aix-Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France. E-mails: [email protected], [email protected]
Abstract: 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.
Keywords: Diffusion equation, distributed order time-fractional derivative, initial boundary value problem, small-time and large-time energy estimates
