Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592615 | Journal of Functional Analysis | 2006 | 32 Pages |
Abstract
In general settings, applying evolutional semigroup arguments, we prove the existence and uniqueness of LpLp-solutions to semi-linear SPDEs of the typedu(t,x)=[Lu(t,x)+f(t,x,u(t))]dt+∑kgk(t,x,u(t))dwtk,u(0,x)=u0(x),x∈E, where LL is an unbounded linear negative operator on Lp(E,B,μ)Lp(E,B,μ), {wtk;t⩾0,k=1,2,…} is a sequence of independent Brownian motions, and (E,B,μ)(E,B,μ) is a general measure space. We also discuss the regularities of solutions in Sobolev spaces. Moreover, a time discretized approximation for above equation is proved to convergence in Hölder spaces. As applications, we study several classes of solutions for different types SPDEs on abstract Wiener space and Riemannian manifold.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xicheng Zhang,