Exponential Attractors for a Doubly Nonlinear Equation

Attractors for a Class of Doubly Nonlinear Parabolic Systems

In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in [L(Ω)] and 2 ∏ i=1 B 1+σi,pi ∞ (Ω).

Uniform Exponential Attractors for a Singularly Perturbed Damped Wave Equation

Our aim in this article is to construct exponential attractors for singularly perturbed damped wave equations that are continuous with respect to the perturbation parameter. The main difficulty comes from the fact that the phase spaces for the perturbed and unperturbed equations are not the same; indeed, the limit equation is a (parabolic) reaction-diffusion equation. Therefore, previous constr...

Exponential Stability in a Nonlinear String Equation

We study the nonlinear wave equation utt ? c 2 uxx = (u) u(0; t) = 0 = u(; t) (0.1) with an analytic nonlinearity of the type (u) = u 3 + P k4 k u k. On each small{energy surface we consider a solution of the linearized system with initial datum having the proole of an elliptic sinus: we show that solutions starting close to the corresponding phase space trajectory remain close to it for times ...

Exponential stability for a nonlinear functional differential equation

Attractors for the semiflow associated with a class of doubly nonlinear parabolic equations

A doubly nonlinear parabolic equation of the form α(ut)−∆u+W (u) = f , complemented with initial and either Dirichlet or Neumann homogeneous boundary conditions, is addressed. The two nonlinearities are given by the maximal monotone function α and by the derivative W ′ of a smooth but possibly nonconvex potential W ; f is a known source. After defining a proper notion of solution and recalling ...