Semilinear parabolic partial differential equations - theory,
approximation, and application

Stig Larsson

New Trends in the Mathematical and Computer Sciences 
(G. O. S. Ekhaguere, C. K. Ayo, and M. B. Olorunsaiye, eds.),
Proceedings of an international workshop at 
Covenant University, Ota, Nigeria, June 18-23, 2006, 
Publications of the ICMCS, vol. 3, 2006, pp. 153-194.  
ISBN: 978-37246-2-2


Abstract. 

We present an abstract framework for semilinear parabolic problems
based on analytic semigroup theory.  The same framework is used for
numerical discretization based on the finite element method.  We prove
local existence of solutions and local error estimates. These are
applied in the context of dynamical systems.  The framework is also
used to analyze the finite element method for a stochastic parabolic
equation.