Semilinear stochastic heat equations perturbed by cubic-type nonlinearities and additive space-time noise with homogeneous boundary conditions are discussed in R^1. The space-time noise is supposed to be Gaussian in time and possesses a Fourier expansion in space along the eigenfunctions of underlying Lapace operators. We follow the concept of approximate strong (classical) Fourier solutions. The existence of unique continuous L^2-bounded solutions is proved. Furthermore, we present a procedure for its numerical approximation based on nonstandard methods (linear-implicit) and justify their stability and consistency. The behavior of related total energy functional turns out to be crucial in the presented analysis.
Published September 25, 2010.
Math Subject Classifications: 34F05, 35R60, 37H10, 37L55, 60H10, 60H15, 65C30.
Key Words: Semilinear stochastic heat equations; cubic nonlinearities; additive noise; homogeneous boundary conditions; approximate strong solution; Fourier expansion; SPDE; existence; uniqueness; energy; Lyapunov functionals; numerical methods; consistency; stability.
Show me the PDF file (259K), TEX file, and other files for this article.
| Henri Schurz |
Department of Mathematics
Southern Illinois University, Carbondale (SIUC)
Carbondale, IL 62901-4408, USA
Return to the table of contents
for this conference.
Return to the EJDE web page