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.
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 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.
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.
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.
This paper is devoted to the global attractors of the tropical climate model. We first establish the global well-posedness of the system. Then by studying the existence of bounded absorbing sets, the global attractor is constructed. The estimates of the Hausdorff dimension and of the fractal dimension of the global attractor are obtained in the end.
In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a solution and its stability with certain small initial and boundary data.