%0 Journal Article
%T Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1
%A Henri Schurz
%J Electronic Journal of Differential Equations
%D 2010
%I Texas State University
%X 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.
%K Semilinear stochastic heat equations
%K cubic nonlinearities
%K additive noise
%K homogeneous boundary conditions
%K approximate strong solution
%K Fourier expansion
%K SPDE
%K existence
%K uniqueness
%K energy
%K Lyapunov functionals
%K numerical methods
%K consistency
%K stability
%U http://ejde.math.txstate.edu/conf-proc/19/s1/abstr.html