SPDE in Hilbert Space with Locally Monotone Coefficients
نویسندگان
چکیده
The aim of this paper is to extend the usual framework of SPDE with monotone coefficients to include a large class of cases with merely locally monotone coefficients. This new framework is conceptually not more involved than the classical one, but includes many more fundamental examples not included previously. Thus our main result can be applied to various types of SPDEs such as stochastic reaction-diffusion equations, stochastic Burgers type equation, stochastic 2-D Navier-Stokes equation, stochastic p-Laplace equation and stochastic porous media equation with non-monotone perturbations. AMS Subject Classification: 60H15, 37L30, 34D45
منابع مشابه
Graph-distance Convergence and Uniform Local Boundedness of Monotone Mappings
In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uni...
متن کاملQuasiconformal Geometry of Monotone Mappings
This paper concerns a class of monotone mappings in a Hilbert space that can be viewed as a nonlinear version of the class of positive invertible operators. Such mappings are proved to be open, locally Hölder continuous, and quasisymmetric. They arise naturally from the Beurling-Ahlfors extension and from Brenier’s polar factorization, and find applications in the geometry of metric spaces and ...
متن کاملStochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered. The coefficients are assumed to have linear growth. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differentia...
متن کاملCoherent Frames
Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...
متن کاملLinear - Implicit Strong Schemes for Ito - Galkerin Approximations of Stochastic Pdes
Linear-implicit versions of strong Taylor numerical schemes for finite dimensional It6 stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an 7 strong linear-implicit Taylor scheme with time-step A applied to the N dimensional It6-Galerkin SDE for a class of parabolic stochastic partial diff...
متن کامل