Approximation of Nonlinear and Functional PDEs
Organizer
Henryk Leszczynski
Institute of Mathematics, University of Gdansk, ul. Wita Stwosza
57, 80-952 Gdansk, Poland
hleszcz@ksinet.univ.gda.pl
Minisymposium abstract
The minisymposium Approximation of Nonlinear and Functional PDEs is
aimed at two aspects of any numerical treatment of partial differential
equations: nonlinearities and functional dependence. We expect that some
of presentations will touch finite difference methods, error analysis,
convergence rate and a priori estimates of solutions. It is our concern
to find new approximation methods in hydrodymamics and engineering. We
are interested in various types of solutions: from analytic functions to
viscosity solutions and solutions with jumps (impulses). As for particular
types of equations, we think of first order equations, second order parabolic
and hyperbolic problems (also higher order), Navier-Stokes equations and
degenerate first-order problems with functional dependence. The main examples
of functional relations are delays and integral operators. Their further
generalization is z(.) , z(t,.) and the
Hale-type operator z(t,x) such that
z(t,x)(s,y)=z(t+s,x+y) .
We are especially fond of the latter model, because it reflects both: local
properties of solutions and simplicity of stating the whole problem in
terms of this operator.
Presentations