报告一题目：Theoretical and numerical analysis of a time-fractional diffusion equation
报告人：Martin Stynes, Beijing Computational Science Research Center, China
Martin Stynes was a Lecturer at Waterford Regional Technical College, Ireland from 1979 to 1984. He then moved to University College Cork, where he was successively Lecturer, Statutory Lecturer, Professor (Scale 2) — these are the equivalents of assistant/associate/full professor. He was a Fulbright Research Professor at Kent State University (USA) in 1990, Royal Society Visiting Fellow at Oxford University (U.K.) in 1991, Visiting Professor at University of Colorado at Denver (USA) in 1997, DFG Visiting Professor at Otto von Guericke University Magdeburg (Germany) in 1998, Visiting Professor at the University of South Carolina (USA) in 2004, and DFG Mercator Guest Professor at the Technical University of Dresden (Germany) in 2008. He was the elected President of the UK and Republic of Ireland Section of SIAM 2003-5. He serves on the editorial boards of the journals “Advances in Computational Mathematics”, “Computational Methods in Applied Mathematics” and “Mathematical Proceedings of the Royal Irish Academy". He took early retirement from University College Cork in 2012 in order to concentrate on research. He has been at CSRC since 2014.
摘要：A reaction-diffusion initial-boundary problem with a Caputo time derivative of order αin (0,1) is considered. The solution of such a problem is discussed; it is shown that in general the solution has a weak singularity near the initial time t=0, and sharp pointwise bounds on the derivatives of this solution are derived. These bounds are then used in a new analysis of a standard finite difference method for the problem. This numerical analysis reveals how to choose a suitably-graded mesh that will yield an accurate approximate solution of the problem. The talk does not assume that the listener is familiar with fractional-order derivatives. It concentrates more on the properties of the solution of the differential equation than on the analysis of the numerical method. The second (shorter) part of the talk assumes that the listener has a little knowledge of finite difference methods for solving differential equations.
M.Stynes, E.O'Riordan and J.L.Gracia, Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation, SIAM J. Numer. Anal. 55 (2017), 1057--1079. DOI: 10.1137/16M1082329
报告二题目：Monotonic iteration positive symmetric solutions to a boundary value problem with p-Laplacian and Stieltjes integral boundary conditions
摘要：This paper investigates the existence of monotonic iteration positive symmetric
solutions to a boundary value problem with p-Laplacian and Stieltjes integral boundary conditions. The main tool is a monotone iterative technique. Meanwhile, an example is worked out to demonstrate the main results.