Time fractional diffusion equations: solution concepts, regularity and long-time behaviour

Abstract

In this paper we give a survey of results on various analytical aspects of time fractional diffusion equations. We describe the approach via abstract Volterra equations and collect results on strong solutions in the $L_p$ sense. We further discuss the concept of weak solutions for equations with rough coefficients and give an account of recent developments towards a De Giorgi-Nash-Moser theory for such equations. The last part summarizes recent results on the long-time behaviour of solutions, which turns out to be significantly different from that in the heat equation case.

19 pages

References in corpus (2)

• Distributed Order Calculus and Equations of Ultraslow Diffusion
• An $L_q(L_p)$-theory for the time fractional evolution equations with variable coefficients

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