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We develop the attractors theory for the semigroups with multidimensional time belonging to some closed cone in an Euclidean space and apply the obtained general results to partial differential equations (PDEs) in unbounded domains. The…
We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. The dissipative character of our model…
The aim of this paper is to prove the existence and qualitative property of random attractors for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) on a semi-infinite interval with a Dirichlet boundary condition on the…
Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then…
In this paper, we first introduce the definitions of random evolutionary system that associate with random evolutionary semigroup and the corresponding global weak or strong random attractor. Then we establish the existence result about…
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…
Discrete Ginzburg-Landau (DGL) equations with non-local nonlinearities have been established as significant inherently discrete models in numerous physical contexts, similar to their counterparts with local nonlinear terms. We study two…
We consider a Large Eddy Simulation model for a homogeneous incompressible Newtonian fluid in a box space domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom…
This paper considers the dynamical behavior of solutions of constitutive systems for 1D compressible viscous and heat-conducting micropolar fluids. With proper constraints on initial data, we prove the existence of global attractors in…
This paper is concerned with the long-time behavior of solutions for the three dimensional primitive equations of large-scale ocean and atmosphere dynamics in an unbounded domain. Since the Sobolev embedding is no longer compact in an…
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.…
The long-time asymptotics is analyzed for all finite energy solutions to a model $\mathbf{U}(1)$-invariant nonlinear Dirac equation in one dimension, coupled to a nonlinear oscillator: {\it each finite energy solution} converges as…
We state necessary and sufficient conditions for the existence of $T$-discrete exponential attractors for semigroups in complete metric spaces. These conditions are formulated in terms of a covering condition for iterates of the absorbing…
This paper proposes an abstract theory concerned with dynamical systems generated by doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations in a reflexive Banach space setting. In order to…
In this paper, we consider the semilinear wave equation involving the nonlinear damping term $g(u_t) $ and nonlinearity $f(u)$. The well-posedness of the weak solution satisfying some additional regularity is achieved under the wider ranges…
Well-posedness and global attractor are established for 2D damped driven nonlinear Schr\"odinger equation with almost periodic pumping in a bounded region. The key role is played by a novel application of the energy equation.
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…
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 $H$…
This paper reports the 3D planetary geostrophic viscous model has the exponential ergodicity and global attractor if this model is driven by an additive random noise, which results in the support of the integration of invariant measure for…
The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…