Weekly Activities

Determination of the fractional order in quasilinear subdiffusion equations
Speaker: Sergei Pereverzev (RICAM, Austria)

Time: 9h30, Tuesday, November 26, 2019
Location: Room 302, Building A5, Institute of Mathematics
Abstract: In the last two decades, fractional partial differential equations play a key role in the description of the so-called anomalous phenomena. The signature of an anomalous diffusion is that the mean square displacement of the diffusing species scales as a nonlinear power law in time. However, sometimes a value of the subdiffusion power/order is not given a priori. In the talk we are going to analyze the inverse boundary value-problem to determine the fractional order of non-autonomous quasilinear subdiffusion equations with memory terms from observations of their solutions during small time. We obtain an explicit formula reconstructing the order. Based on the Tikhonov regularization scheme and the quasi-optimality criterion, we construct the computational algorithm to find the order from noisy discrete measurements. We also present several numerical tests illustrating the algorithm in action.

The presentation is based on the joint research with Nataliya Vasylyeva, Mykola Krasnoschok and Sergii Siryk that has been partially supported by Consortium AMMODIT (Approximation Methods for Molecular Modelling and Diagnosis Tools) funded within European Programme Horizon 2020.