Dynamics of Partial Differential Equations

Volume 3 (2006)

Number 3

Nonautonomous semilinear parabolic equations on an infinite interval

Pages: 209 – 233

DOI: https://dx.doi.org/10.4310/DPDE.2006.v3.n3.a3

Author

Jason R. Morris (Department of Mathematics, University of Pittsburgh, Pittsburgh, Penn.)

Abstract

The topological degree for Fredholm operators is used to prove the existence of solutions to a class of semilinear parabolic partial differential equations on an infinite time interval. General initial conditions are allowed and homogeneous Dirichlet boundary conditions are assumed. The solutions are shown not only to exist for all times, but also to be L^p in time and space.

Keywords

topological degree, Fredholm operator, Dirichlet boundary condition, semilinear parabolic partial differential equation

2010 Mathematics Subject Classification

Primary 35K55. Secondary 35B40, 35B45, 47H11.

Published 1 January 2006