Global attractors for the complex Ginzburg–Landau equation

Global Attractors for a Semilinear Hyperbolic Equation in Viscielasticity

A semilinear partial differential equation of hyperbolic type with a convolution term describing simple viscoelastic materials with fading memory is considered. Ž . Regarding the past history memory of the displacement as a new variable, the equation is transformed into a dynamical system in a suitable Hilbert space. The dissipation is extremely weak, and it is all contained in the memory term....

Attractors for the Viscous Camassa-holm Equation

Abstract. We consider the viscous Camassa-Holm equation subject to an external force, where the viscosity term is given by second order differential operator in divergence form. We show that under some mild assumptions on the viscosity term, one has global wellposedness both in the periodic case and the case of the whole line. In the periodic case, we show the existence of global attractors in ...

Periodic attractors for the varactor equation

We consider a class of differential equations, ẍ + γẋ + x = f(ωt), with p ∈ N and ω ∈ R, describing one-dimensional dissipative systems subject to a periodic forcing. For p = 1 the equation describes a resistor-inductor-varactor circuit, hence the name ‘varactor equation’. We concentrate on the limit cycle described by the trajectory with the same period as the forcing; numerically, for γ large...

Existence of Global Attractors for the Nonlinear Plate Equation with Memory Term

Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation

We study the asymptotic behavior of solutions of discrete nonlinear Schrödinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the question of existence of standing wave solutions. Similarities and differences with the continuous counterpart (NLS-partial differential equation) are pointed out. For a dissipative system we prove existence of a glo...