Existence of random attractors for the floating beam equation with strong damping and white noise

Existence of Random Attractors for a p-Laplacian-Type Equation with Additive Noise

and Applied Analysis 3 introducing a new inner product over the resolvent of Laplacian, we surmount this obstacle and obtain the estimate of the solution in the Sobolev space V0, which is weaker than V , see Lemma 4.2 in Section 4. Here some basic results about Dirichlet forms of Laplacian are used. For details on the Dirichlet forms of a negative definite and self-adjoint operator please refer...

Existence of Exponential Attractors for the Plate Equations with Strong Damping

We show the existence of (H2 0 (Ω)×L2(Ω), H2 0 (Ω)×H2 0 (Ω))-global attractors for plate equations with critical nonlinearity when g ∈ H−2(Ω). Furthermore we prove that for each fixed T > 0, there is an (H2 0 (Ω) × L2(Ω), H2 0 (Ω) × H2 0 (Ω))T -exponential attractor for all g ∈ L2(Ω), which attracts any H2 0 (Ω)×L2(Ω)-bounded set under the stronger H2(Ω)×H2(Ω)-norm for all t ≥ T .

Limiting behavior of global attractors for singularly perturbed beam equations with strong damping

The limiting behavior of global attractors Aε for singularly perturbed beam equations ε ∂u ∂t2 + εδ ∂u ∂t + A ∂u ∂t + αAu+ g(‖u‖ 1/4)A u = 0 is investigated. It is shown that for any neighborhood U of A0 the set Aε is included in U for ε small.

Criteria for strong and weak random attractors

The notion of an attractor is one of the basic concepts in the theory of dynamical systems. For deterministic systems this notion has been of importance since several decades. Since about fifteen years also attractors for stochastic systems have been taken under consideration. The crucial obstacle came from the fact that the classical approach, using the Markov property of individual solutions ...

Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise.