Related papers: Invariant manifolds for stochastic delayed partial…
This work deals with the dynamics of a class of stochastic dynamical systems with a multiplicative non-Gaussian Levy noise. We first establish the existence of stable and unstable foliations for this system via the Lyapunov-Perron method.…
In this paper we study high order expansions of chart maps for local finite dimensional unstable manifolds of hyperbolic equilibrium solutions of scalar parabolic partial differential equations. Our approach is based on studying an…
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all…
In this paper we consider the stability for a type of stochastic McKean-Vlasov equations with non-Lipschitz coefficients. First, sufficient conditions are given for the exponential stability of the second moments for their solutions in…
Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic--parabolic system of conservation laws possesses a translation-invariant center…
We present a reduced system of 7 ordinary differential equations that captures the time evolution of spatial gradients of the velocity and the temperature in fluid elements of stratified turbulent flows. We show the existence of invariant…
We prove existence and uniqueness of an unstable manifold for a degenerate hyperbolic map of the plane arising in statistics.
We study the well-posedness and the long-time behavior of almost periodic solutions to stochastic degenerate parabolic-hyperbolic equations in any space dimension, under the assumption of Lipschitz continuity of the flux and viscosity…
We give a new, two-step approach to prove existence of finite invariant measures for a given Markovian semigroup. First, we identify a convenient auxiliary measure and then we prove conditions equivalent to the existence of an invariant…
We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The problem of reduced description is studied as a problem of constructing the slow…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
Let $\overline{M}$ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric $g$. Let $\overline{M}_\Gamma$ be a Galois $\Gamma$-covering. Under additional assumptions on $\overline{M}$, satisfied for example by Witt…
We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…
We construct stable manifolds for a class of degenerate evolution equations including the steady Boltzmann equation, establishing in the process exponential decay of associated kinetic shock and boundary layers to their limiting equilibrium…
We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform…
We investigate the existence of stationary fronts in a coupled system of two sine-Gordon equations with a smooth, "hat-like" spatial inhomogeneity. The spatial inhomogeneity corresponds to a spatially dependent scaling of the sine-Gordon…
Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in…
Our aim in this paper is to establish stable manifolds near hyperbolic equilibria of fractional differential equations in arbitrary finite dimensional spaces.
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…