Related papers: Averaging principle and hyperbolic evolution equat…
Averaging principle for abstract non-autonomous parabolic evolution equations governed by time-dependent family of positive sectorial operators is proved. Apart from linear case also a nonlinear version for continuous perturbations is…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
Kato's theory on the construction of strongly continuous evolution systems associated with hyperbolic equations is applied to the linear equation describing an age-structured population that is subject to time-dependent diffusion. The…
We study the validity of an averaging principle for a slow-fast system of stochastic reaction diffusion equations. We assume here that the coefficients of the fast equation depend on time, so that the classical formulation of the averaging…
Averaging principle is an effective method for investigating dynamical systems with highly oscillating components. In this paper, we study three types of averaging principle for stochastic complex Ginzburg-Landau equations. Firstly, we…
The averaging principle is established for the slow component and the fast component being two dimensional stochastic Navier-Stokes equations and stochastic reaction-diffusion equations, respectively. The classical Khasminskii approach…
We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…
We establish an averaging principle on the real semi-axis for semi-linear equation \begin{equation}\label{eqAb1} x'=\varepsilon (\mathcal A x+f(t)+F(t,x))\nonumber \end{equation} with unbounded closed linear operator $\mathcal A$ and…
In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of…
This work concerns about forward-backward multivalued stochastic systems. First of all, we prove one average principle for general stochastic differential equations in the $L^{2p}$ ($p\geq 1$) sense. Moreover, for $p=1$ a convergence rate…
We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential…
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
In this work we study the averaging principle for non-autonomous slow-fast systems of stochastic differential equations. In particular in the first part we prove the averaging principle assuming the sublinearity, the Lipschitzianity and the…
An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…
Typically, models with a heterogeneous property are considerably harder to analyze than the corresponding homogeneous models, in which the heterogeneous property is replaced with its average value. In this study we show that any outcome of…
Typically, models with a heterogeneous property are considerably harder to analyze than the corresponding homogeneous models, in which the heterogeneous property is replaced with its average value. In this study we show that any outcome of…
In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations…
By using the technique of the Zvonkin's transformation and the classical Khasminkii's time discretization method, we prove the averaging principle for slow-fast stochastic partial differential equations with bounded and H\"{o}lder…
The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An example is constructed to show that the averaged coefficients may become…