Attractor for Dissipative Klein–Gordon–Schrödinger Equations inR3

Stochastic Weak Attractor for a Dissipative Euler

Exponential Attractor for a First-Order Dissipative Lattice Dynamical System

Lattice systems arise in many applications, for example, in chemical reaction theory, image processing, pattern recognition, material science, biology, electrical engineering, laser systems, and so forth. A lattice dynamical system LDS is an infinite system of ordinary differential equations lattice ODEs or of difference equations. In some cases, they arise from spatial discretizations of parti...

Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity

In order to study the longtime behavior of a dissipative evolutionary equation, we generally aim to show that the dynamics of the equation is finite dimensional for long time. In fact, one possible way to express this fact is to prove that dynamical systems describing the evolutional equation comprise the existence of the global attractor 1 . The KDV equation without dissipative and forcing was...

Dissipative Boussinesq equations

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated nu...

Decay Rates for Dissipative Wave equations

We derive decay rates for the energy of solutions of dissipative wave equations. The metod of proof combines multiplier techniques and the construction of suitable Lyapunov functionals. Without imposing any growth condition at the origin on the nonlinearity we show that this Lyapunov functional, which is equivalent to the energy of the system, is bounded above by the solution of a differential ...