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This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by Lévy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then, the existence and uniqueness of weak pullback mean random attractors for the equations are established by defining a mean random dynamical system. Next, we prove the existence of invariant measures when the problem is autonomous by means of the fact that Hγ (Ϭ) is compactly embedded in L²(Ϭ) with γ γ (0, 1). Moreover, the uniqueness of this invariant measure is presented, which ensures the ergodicity of the problem. Finally, a large deviation principle result for solutions of stochastic PDEs perturbed by small Lévy noise and Brownian motion is obtained by a variational formula for positive functionals of a Poisson random measure and Brownian motion. Additionally, the results are illustrated by the fractional stochastic Chafee-Infante equations. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the well-posedness and asymptotic behavior of a class of stochastic nonlocal partial differential equations driven by nonlinear noise. First, the existence of a weak martingale solution is established by using the Faedo—Galerkin approximation and an idea analogous to Da Prato and Zabczyk [Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992]. Second, we show the uniqueness and continuous dependence on initial values of solutions to the above stochastic nonlocal problem when there exist some variational solutions. Third, the asymptotic local stability of steady-state solutions is analyzed either when the steady-state solution of the deterministic problem is also a solution of the stochastic one or when this does not happen. Next, to study the global asymptotic behavior, namely, the existence of attracting sets of solutions, we consider an approximation of the noise given by Wong and Zakai's technique using the so called colored noise. For this model, we can use the power of the theory of random dynamical systems and prove the existence of random attractors. Eventually, particularizing in the cases of additive and multiplicative noise, it is proved that the Wong—Zakai approximation models possess random attractors which converge upper-semi-continuously to the respective random attractors of the stochastic equations driven by standard Brownian motions. This fact justifies the use of this colored noise technique to approximate the asymptotic behavior of the models with general nonlinear noises, although the convergence of attractors and solutions is still an open problem. [ABSTRACT FROM AUTHOR]

We analyze the well-posedness of two versions of a stochastic time delay fractional 2D-Stokes model with nonlinear multiplicative noise. The main tool to prove the existence and uniqueness of mild solutions is a fixed point argument. The results for the first model can only be proved for α ∈ (1/2, 1), and the global existence in time is shown only when the noise is additive. As for the second model, all results are true for α ∈ (0, 1), and the global solutions in time is shown for general nonlinear multiplicative noise. The analyzes for the finite and infinite delay cases, follow the same lines, but they require different phase spaces and estimates. This article can be considered as a first approximation to the challenging model of stochastic time fractional Navier-Stokes (with or without delay) which so far remains as an open problem. [ABSTRACT FROM AUTHOR]

A soybean MADS box gene Gm GAL2 ( Glycine max AGAMOUS Like 2), a homolog of AGL11/ STK, was investigated in transgenic Arabidopsis lines. Ectopic expression of Gm GAL2 in Arabidopsis enhanced flowering, under both long-day and short-day conditions, by promoting expression of key flowering genes, CONSTANS ( CO) and FLOWERING LOCUS T ( FT), and lowering expression of floral inhibiter FLOWERING LOCUS C ( FLC). Moreover, frequency of silique pod set was also lower in transgenic compared to control Arabidopsis plants. RT-PCR results revealed that Gm GAL2 was primarily expressed in the flowers and pods of soybean plants, Gm GAL2 expressed higher in SD than LD in soybean. [ABSTRACT FROM AUTHOR]