Related papers: Finite-dimensional global and exponential attracto…
We consider Cauchy problem for the semilinear plate equation with nonlocal nonlinearity. Under mild conditions on the damping coefficient, we prove that the semigroup generated by this problem possesses a global attractor.
The characterization of global solutions to the obstacle problems in $\mathbb{R}^N$, or equivalently of null quadrature domains, has been studied over more than 90 years. In this paper we give a conclusive answer to this problem by proving…
We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions. Under reasonable hypotheses, we establish the existence of component wise…
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…
In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy's law. We show formation of singularities with infinite energy and for finite energy we obtain…
This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H.…
In this work, we carry out the asymptotic analysis of the two dimensional convective Brinkman-Forchheimer (CBF) equations, which characterize the motion of incompressible fluid flows in a saturated porous medium. We establish the existence…
We consider a nonlocal nonlinear model with fractional diffusion motivated by studies of electroconvection phenomena in incompressible viscous fluids. We address the global well-posedness, global regularity and long time dynamics of the…
Global existence of strong solutions and the existence of global and atrractors are established for generalized Shigesada-Kawasaki-Teramoto models on planar domains. The cross diffusion and reaction can have polynomial growth of any order.
P. Galenko et al. proposed a modified Cahn-Hilliard equation to model rapid spinodal decomposition in non-equilibrium phase separation processes. This equation contains an inertial term which causes the loss of any regularizing effect on…
In this article, we prove the finite dimensionality of the global attractor and estimate the numbers of the determining modes for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case.
Let $\Lambda$ be a complete metric space, and let $\{S_\lambda(\cdot):\ \lambda\in\Lambda\}$ be a parametrised family of semigroups with global attractors ${\mathscr A}_\lambda$. We assume that there exists a fixed bounded set $D$ such that…
We consider the subcritical SQG equation in its natural scale invariant Sobolev space and prove the existence of a global attractor of optimal regularity. The proof is based on a new energy estimate in Sobolev spaces to bootstrap the…
This article addresses the issue of uniform measure attractors for non-autonomous McKean-Vlasov stochastic reaction-diffusion equations defined on unbounded thin domains. Initially, the concept of uniform measure attractors is recalled, and…
In this work we obtain theoretical results on continuity of selected pullback attractors and we apply them to reaction diffusion equations with dynamical boundary conditions
Global dynamics of nonautonomous diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain in neurodynamics is investigated. The existence of a pullback attractor is proved through uniform estimates showing the pullback…
We study a two-phase modified Stefan problem modeling solid combustion and nonequilibrium phase transition. The problem is known to exhibit a variety of non-trivial dynamical scenarios. We develop a priori estimates and establish…
In this paper, we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term $f$ fulfills the polynomial growth of arbitrary order and the external force $ g(x)\in…
In this paper, we apply an implicit Euler scheme to discretize the complex Ginzburg-Landau equation and prove the existence of a numerical attractor for the discrete Ginzburg-Landau system. We establish the upper semicontinuity of the…
In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We consider two cases, depending on the values of the parameters…