Large Deviations for Stochastic Reaction–diffusion Systems with Multiplicative Noise and Non-lipschitz Reaction Term1 by Sandra Cerrai
نویسنده
چکیده
Following classical work by Freidlin [Trans. Amer. Math. Soc. (1988) 305 665–657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504–537] and Peszat [Probab. Theory Related Fields (1994) 98 113–136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction–diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, assuming the reaction terms to be only locally Lipschitz with polynomial growth. This generalizes results of the above mentioned authors. Our results apply, in particular, to systems of stochastic Ginzburg–Landau equations with multiplicative noise.
منابع مشابه
Stochastic reaction - diffusion systems with multiplicative noise and non - Lipschitz reaction term
We study existence and uniqueness of a mild solution in the space of continuous functions and existence of an invariant measure for a class of reaction-diffusion systems on bounded domains of R , perturbed by a multiplicative noise. The reaction term is assumed to have polynomial growth and to be locally Lipschitz-continuous and monotone. The noise is white in space and time if d = 1 and colour...
متن کاملLarge deviations for invariant measures of stochastic reaction–diffusion systems with multiplicative noise and non-Lipschitz reaction term
In this paper we prove a large deviations principle for the invariant measures of a class of reaction–diffusion systems in bounded domains of Rd , d 1, perturbed by a noise of multiplicative type. We consider reaction terms which are not Lipschitzcontinuous and diffusion coefficients in front of the noise which are not bounded and may be degenerate. This covers for example the case of Ginzburg–...
متن کاملKhasminskii type averaging principle for stochastic reaction - diffusion equations ∗ Sandra Cerrai Dip . di Matematica per le Decisioni Università di Firenze Via C . Lombroso 6 / 17 I - 50134 Firenze , Italy
We prove that an averaging principle holds for a general class of stochastic reactiondiffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite dimensional systems.
متن کاملAveraging Principle for Systems of Reaction-Diffusion Equations with Polynomial Nonlinearities Perturbed by Multiplicative Noise
We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.
متن کاملStabilization by noise for a class of stochastic reaction-diffusion equations
Abstract. We prove uniqueness, ergodicity and strongly mixing property of the invariant measure for a class of stochastic reaction-diffusion equations with multiplicative noise, in which the diffusion term in front of the noise may vanish and the deterministic part of the equation is not necessary asymptotically stable. To this purpose, we show that the L1-norm of the difference of two solution...
متن کامل