CAS Seminar

Jichen Yang

(Universit├Ąt Bremen)

"Spectral analysis and decay estimates for reaction-subdiffusion equations"

Date: Tue, December 3, 2019
Time: 14:15
Place: Research I, Room 103

Abstract: The modelling of reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time fractional derivative. It is known that the precise form depends on the interaction of dispersal and reaction, and leads to qualitative differences. We refine these results by defining generalised spectra through dispersion relations, which allows us to examine the stability and onset of instability and in particular inspect Turing type instabilities. Moreover, we show that one class of reaction-subdiffusion equations algebraic decays for stable spectrum, whereas for another class this is exponential.