Domain Perturbation for Parabolic Equations

                                   by

                             Daniel Daners

               JWB 335, 3:10pm  Monday, December 11, 1995

                                Abstract

   We present a general theory of domain perturbation for linear and
   nonlinear parabolic equations on arbitrary domains subject to
   Dirichlet boundary conditions. The results show that even very
   singular perturbations of a domain such as for instance adding small
   pieces or cutting holes are small perturbations. We consider the
   initial value problem for the nonautonomous parabolic equation with
   bounded and measurable coefficients and shortly discuss
   periodic-parabolic problems. We outline how the theory can be used to
   show that certain nonlinear periodic-parabolic equations have
   multiple periodic solutions.


Requests for reprints and preprints to daners_d@maths.su.oz.au