相关论文: Global Dynamics of Nonautonomous Hindmarsh-Rose Eq…
Global dynamics of the diffusive and partly diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in neurodynamics are investigated in this paper. The existence of global attractors as well as the regularity…
The longtime and global pullback dynamics of stochastic Hindmarsh-Rose equations with multiplicative noise on a three-dimensional bounded domain in neurodynamics is investigated in this work. The existence of a random attractor for this…
The existence of an exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in the study of neurodynamics is proved through uniform estimates together with a new theorem on the…
Global dynamics of the diffusive Hindmarsh-Rose equations with memristor as a new proposed model for neuron dynamics are investigated in this paper. We prove the existence and regularity of a global attractor for the solution semiflow…
For stochastic Hindmarsh-Rose equations with additive noises in the study of neurodynamics, the longtime and global pullback dynamics on a two-dimensional bounded domain is explored in this work. Using the additive transformation and by the…
We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space R^n when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation…
This paper concerns the tempered pullback dynamics of 2D incompressible non-autonomous Navier-Stokes equation with non-homogeneous boundary condition on Lipschitz-like domain. With the presence of a time-dependent external force f(t) which…
The purpose of this paper is to investigate the existence and Hausdorff dimension as well as fractal dimension of global attractors for a delayed reaction-diffusion equation on an unbounded domain. The noncompactness of the domain causes…
We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one…
The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal dimension of global attractors for a delayed reaction-diffusion equation on an unbounded domain. The noncompactness of the domain cause the…
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors…
We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…
This paper is concerned with pullback dynamics of 3D Navier-Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a…
This paper is concerned with the long-time behavior of solutions for the three dimensional globally modified Navier-Stokes equations in a three-dimensional bounded domain. We prove the existence of a global attractor $\mathcal{A}_0$ in $H$…
We study the asymptotic behavior of solutions of discrete nonlinear Schr\"odinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the question of existence of standing wave solutions.…
In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well-known, and the…
If the semigroup is slowly non-dissipative, i.e., its solutions can diverge to infinity as time tends to infinity, one still can study its dynamics via the approach by the unbounded attractors - the counterpart of the classical notion of…
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…
We extend the Lyapunov function technique, a fundamental tool for investigating asymptotic stability and existence of attractors for ordinary differential equations, by introducing the notion of a {\it strong Lyapunov function} for an…