Nonautonomous semilinear parabolic equations on an infinite interval
Jason R. Morris · Dynamics of Partial Differential Equations · 2006
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.