[hal-00668272, v1] Strong solutions to semilinear SPDEs
نویسنده
چکیده
Abstract. We study the Cauchy problem for a semilinear stochastic partial differential equation driven by a finite-dimensional Wiener process. In particular, under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives, we consider the equation in the context of power scale generated by a strongly elliptic differential operator. Application of semigroup arguments then yields the existence of a continuous strong solution.
منابع مشابه
Structural properties of semilinear SPDEs driven by cylindrical stable processes
Abstract: We consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise. We investigate structural properties of the solutions like Markov, irreducibility, stochastic continuity, Feller and strong Feller properties, and study integrability of trajectories. The obtained results can be applied to semilinear stochastic heat equations with Dirichlet...
متن کاملStochastic Volterra Equations in Banach Spaces and Stochastic Partial Differential Equations*
In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then, we apply them to a large class of semilinear stochastic partial differential equations (SPDE) driven by Brownian motions as well as by fractional Brownian motions, and obtain the existence of unique max...
متن کاملSome Refinements of Existence Results for Spdes Driven by Wiener Processes and Poisson Random Measures
We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear growth (or local boundedness, resp.) conditions. The socalled “method of the moving frame” allows us to reduce the SPDE problems to SDE problems.
متن کامل[hal-00359844, v1] Homogenization of periodic semilinear parabolic degenerate PDEs
(a) LERSTAD, UFR S.A.T, Université Gaston Berger, BP 234, Saint-Louis, SENEGAL. email : [email protected] (b) CEREMADE, Université Paris-Dauphine, Place du maréchal De Lattre de Tassigny, 75775 Paris cedex 16, FRANCE. email : [email protected] (c) CMI, LATP-UMR 6632, Université de Provence, 39 rue F. Joliot Curie, 13453 Marseille cedex 13, FRANCE. email : [email protected] Abstr...
متن کاملLyapunov exponents of hybrid stochastic heat equations
Stabilization of (ordinary) stochastic differential equations (SDEs) by noise has been studied extensively in the past few years, e.g., Arnold et al. [1], Has’minskii [6], Mao and Yuan [10], Pardoux and Wihstutz [11, 12], Scheutzow [15]. Recently, there are also many works focusing on such phenomena for stochastic partial differential equations (SPDEs), e.g., Kwiecinska [7] and Kwiecinska [9] d...
متن کامل