Dynamics of Partial Differential Equations
Volume 3 (2006)
Nonautonomous semilinear parabolic equations on an infinite interval
Pages: 209 – 233
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 Lp in time and space.
topological degree, Fredholm operator, Dirichlet boundary condition, semilinear parabolic partial differential equation
2010 Mathematics Subject Classification
Primary 35K55. Secondary 35B40, 35B45, 47H11.