Global attractor for an equation modelling a thermostat.
Global attractor for Navier-Stokes equations in cylindrical domains
Global and regular solutions of the Navier-Stokes system in cylindrical domains have already been obtained under the assumption of smallness of (1) the derivative of the velocity field with respect to the variable along the axis of cylinder, (2) the derivative of force field with respect to the variable along the axis of the cylinder and (3) the projection of the force field on the axis of the cylinder restricted to the part of the boundary perpendicular to the axis of the cylinder. With the same...
Global Attractor for the Convective Cahn-Hilliard Equation
This paper is concerned with the convective Cahn-Hilliard equation. We use a classical theorem on existence of a global attractor to derive that the convective Cahn-Hilliard equation possesses a global attractor on some subset of H².
Global Attractor for the Convective Cahn-Hilliard Equation in
We consider the convective Cahn-Hilliard equation with periodic boundary conditions. Based on the iteration technique for regularity estimates and the classical theorem on existence of a global attractor, we prove that the convective Cahn-Hilliard equation has a global attractor in .
Global attractor for the generalized dissipative KdV equation with nonlinearity.
Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation.
Global attractor for the Navier-Stokes equations in a cylindrical pipe
Global existence of regular special solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has already been shown. In this paper we prove the existence of the global attractor for the Navier-Stokes equations and convergence of the solution to a stationary solution.
Global attractor for the perturbed viscous Cahn-Hilliard equation
We consider the initial-boundary value problem for the perturbed viscous Cahn-Hilliard equation in space dimension n ≤ 3. Applying semigroup theory, we formulate this problem as an abstract evolutionary equation with a sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space (H²(Ω)∩ H¹₀(Ω)) × L²(Ω) and characterize its structure.
Global attractors for a class of degenerate diffusion equations.
Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on
We prove the existence of global attractors for the following semilinear degenerate parabolic equation on : ∂u/∂t - div(σ(x)∇ u) + λu + f(x,u) = g(x), under a new condition concerning the variable nonnegative diffusivity σ(·) and for an arbitrary polynomial growth order of the nonlinearity f. To overcome some difficulties caused by the lack of compactness of the embeddings, these results are proved by combining the tail estimates method and the asymptotic a priori estimate method.
Global attractors for two-phase Stefan problems in one-dimensional space.
Global dynamics of a reaction-diffusion system.
Global existence and long-time behavior of solutions to a class of degenerate parabolic equations
We study the global existence and long-time behavior of solutions for a class of semilinear degenerate parabolic equations in an arbitrary domain.
Global φ-attractor for a modified 3D Bénard system on channel-like domains
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.
Hyperbolic Equations in Uniform Spaces
The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of ℝ ⁿ. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space . Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.
Kolmogorov's epsilon-entropy of the attractor of the strongly damped wave equation in locally uniform spaces
We establish an upper bound on the Kolmogorov’s entropy of the locally compact attractor for strongly damped wave equation posed in locally uniform spaces in subcritical case using the method of trajectories.
Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation.
Local attractivity in nonautonomous semilinear evolution equations
We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity...
Long-term damped dynamics of the extensible suspension bridge.
Long-time behavior for 2D non-autonomous g-Navier-Stokes equations
We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force is time-independent...