PDE and Applied Mathematics Seminar

Fall 2016

Organized by Peter Gordon

October 19 (CAS 220D, 2:30-3:30pm) Igor Boglaev (Institute of Fundamental Sciences, Massey University, New Zealand) will speak on "Monotone numerical methods for nonlinear parabolic problems."

Abstract: The talk is concerned with monotone numerical methods for nonlinear parabolic problems. The basic idea of the iterative methods for the computation of numerical solutions is the monotone approach which involves the notion of upper and lower solutions and the construction of monotone sequences from a suitable linear discrete system. The monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration. The monotone convergence property is used to prove the convergence of the nonlinear discrete problems to the corresponding differential problems as mesh sizes decrease to zero. Applications are given to several models arising from physical, chemical and biological systems. Numerical experiments are given to some of these models, including a discussion on a rate of convergence of the monotone sequences.

October 26 (CAS 220D, 2:30-3:30 pm) Paata Ivanisvili (Kent State University) will speak on "Monge-Ampere type equations and their applications to functional isoperimetric inequalities. ."

Abstract: It stayed largely unnoticed that one and the only fully nonlinear PDE but with different initial data lies in the base of many classical functional inequalities. But more importantly, by a careful change of variables coming from exterior differential systems this PDE can be made linear: namely, the inverse heat equation. Then such classical inequalities as log-Sobolev, Poincare, Beckner-Sobolev, Bobkov's inequality become particular solutions of this inverse heat equation. Besides that, this observation allows us to invent new edge-isoperimetric inequalities on the Hamming cube.

Previous seminars:
Spring 2016
Fall 2015
Spring 2015
Fall 2014
Spring 2014
Fall 2013
Spring 2013
Fall 2012