Mathematics Research News

The Mathematics Research Seminar series, organised by the Mathematical Sciences Research Group, provides a forum for members of the group to share their work and for external speakers to present to staff and postgraduate students from the faculty. A list of recent and upcoming seminars and  other news may be found below. 

Mathematics Research Seminar Programme 2016-17

For details of future seminars taking place, please contact Dr Fotini Karakatsani: f.karakatsani@chester.ac.uk.

Seminar Monday 30th January at 17:00-18:00, Room TSU102

Title: Time fractional diffusion systems and their applications in control theory

Speaker: Professor Kou Chunhai from the Donghua University, China

ABSTRACT

Recently anomalous diffusion systems have attracted increasing research interest since the introduction of continuous time random walks (CTRWS) and a large number of contributions have been given to them. The time fractional diffusion system, which replaces the first order time derivative by a fractional derivative, has been seen as the macroscopic presentation of a CTRW model.  From a physical view-point, this generalized diffusion equation can be used to describe transport processes with long memory in the spatially inhomogeneous environment. Here we attempt to explore the boundary feedback stabilization for a class of time fractional diffusion systems. By designing an invertible coordinate transformation, the Mittag-Leffler stability of the system studied is obtained.  Simulation result is also given at last to test the effectiveness of our results.  We hope that the results here could provide some insight into the control theory analysis for the time fractional diffusion system.

 

Seminar Thursday the 24th of November at 12:00-13:00, Room TSU102

Title: Initial/Boundary Value Problems in Soliton Theory: Admissible Data for the Unified Scattering Method

Speaker: Prof. Spyros Kamvissis, from the University of Crete, Greece

ABSTRACT

Initial/boundary value problems for 1-dimensional `completely integrable' equations (NLS, KdV, Sine-Gordon, etc.) can be studied via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the particular case of cubic NLS, for example, knowledge of the Dirichlet data suffices to make the problem well-posed but the Fokas "unified" method also requires knowledge of the values of Neumann data. The study of the Dirichlet to Neumann map is thus necessary before the application of the unified method. In recent work with Dimitra Antonopoulou, we provide a rigorous study of this map for a large class of decaying Dirichlet data. We show that the Neumann data are also sufficiently decaying and hence rigorously justify the applicability of the unified method.

Mathematics Research Seminar Programme 2015-16