Existence and regularity of a global attractor for doubly nonlinear parabolic equations.
Existence and upper semicontinuity of uniform attractors in for nonautonomous nonclassical diffusion equations
We prove the existence of uniform attractors in the space for the nonautonomous nonclassical diffusion equation , ε ∈ [0,1]. The upper semicontinuity of the uniform attractors at ε = 0 is also studied.
Existence of absorbing set for a nonlinear wave equation.
Existence of global attractors in for -Laplacian parabolic equation in .
Existence of global solution for a nonlocal parabolic problem.
Exponential attractor for a first-order dissipative lattice dynamical system.
Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls.
Exponential attractors for a nonclassical diffusion equation.
Extremal equilibria for parabolic non-linear reaction-diffusion equations
Finite dimensional dynamics for Kolmogorov-Petrovsky-Piskunov equation.
Finite dimensional global attractor for a class of doubly nonlinear parabolic equations
Our aim in this paper is to study the long time behavior of a class of doubly nonlinear parabolic equations. In particular, we prove the existence of the global attractor which has, in one and two space dimensions, finite fractal dimension.
Finite dimensional uniform attractors for the nonautonomous Camassa-Holm equations.
Finite fractal dimension of pullback attractors and application to non-autonomous reaction diffusion equations.
Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains
We study the existence and long-time behavior of weak solutions to Newton-Boussinesq equations in two-dimensional domains satisfying the Poincaré inequality. We prove 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.
Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials
Using the asymptotic a priori estimate method, we prove the existence of a pullback -attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of (N ≥ 3), with the nonlinearity of polynomial type and a suitable exponential growth of the external force. Then under some additional conditions, we show that the pullback -attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential.
Global and exponential attractors for a Caginalp type phase-field problem
We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.
Global attraction to solitary waves in models based on the Klein-Gordon equation.
Global Attractor for a Class of Parabolic Equations with Infinite Delay
We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.
Global Attractor for a Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth
This paper is concerned with a fourth-order parabolic equation which models epitaxial growth of nanoscale thin films. Based on the regularity estimates for semigroups and the classical existence theorem of global attractors, we prove that the fourth order parabolic equation possesses a global attractor in a subspace of H², which attracts all the bounded sets of H² in the H²-norm.
Global attractor for a semilinear parabolic equation involving Grushin operator.