相关论文: A note on invariant manifolds for stochastic parti…
We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds for solutions of stochastic partial differential equations (SPDEs) in continuously embedded Hilbert spaces with non-smooth…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential…
The qualitative properties of local random invariant manifolds for stochastic partial differential equations with quadratic nonlinearities and multiplicative noise is studied by a cut off technique. By a detail estimates on the Perron fixed…
In this paper we provide necessary and sufficient conditions for invariance of finite dimensional submanifolds for rough differential equations (RDEs) with values in a Banach space. Furthermore, we apply our findings to the particular…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Invariant manifolds play an important role in the study of the qualitative dynamical behaviors for nonlinear stochastic partial differential equations. However, the geometric shape of these manifolds is largely unclear. The purpose of the…
This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…
In this paper we provide sufficient conditions for stochastic invariance of closed convex cones for stochastic partial differential equations (SPDEs) of jump-diffusion type, and clarify when these conditions are necessary. Our results apply…
We consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions is proved via a fixed-point argument for nondecreasing…
In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…
Invariant foliations are complicated random sets useful for describing and understanding the qualitative behaviors of nonlinear dynamical systems. We will consider invariant foliations for stochastic partial differential equation with…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is…
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…
In this paper, we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions, which can be applied to a large class of SPDE with finite delays, e.g.…
We establish necessary and sufficient conditions for stochastic invariance of closed subsets in Hilbert spaces for solutions to infinite-dimensional stochastic differential equations (SDEs) under mild assumptions on the coefficients. Our…
Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…
Finite dimensional solutions to a class of stochastic partial differential equations are obtained extending the differential constraints method for deterministic PDE to the stochastic framework. A geometrical reformulation of the stochastic…
For a system of partial differential equations (PDEs) $F = 0$ admitting a local (point, contact, or higher) symmetry $X$ with the characteristic $\varphi$, invariant solutions satisfy the reduced system $F = \varphi = 0$. We propose a…