PDE and Applied Mathematics Seminar
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."
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
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. ."
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.