Attractors for Second-Order Evolution Equations with a Nonlinear Damping

By Igor D. Chueshov, Irena Lasiecka. 2004

186 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/336218e0b65c8263b0f7df6d5f2cf46710d92454

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Citations in the corpus

Global attractors for wave equations with nonlinear interior damping and critical exponents (2006, methodology): “But, as mentioned in [1], the detailed proof of this result was not published.”
Long-time dynamics of Kirchhoff wave models with strong nonlinear damping (2010, methodology): “To establish these results we rely on recently developed approach (see [12] and also [13] and [14, Chapters 7,8]) which involves stabilizability estimates, the notion of a quasi-stable system and also the idea of ”short” trajectories due to [29, 30].”
Global Attractors for Mindlin–Timoshenko Plates and for Their Kirchhoff Limits (2006, methodology): “In this paper we would like to demonstrate the approach which has been developed [ 4 , 6] for systems with nonlinear damping.”
Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, methodology): “Another powerful and useful method to prove the finite dimensionality of the global attractor is based on the so-called l-trajectories: one needs minimal regularity on the solutions in order to apply this method, see [32,53,54,152–154,173,190], and [192].”
Global attractors for von Karman equations with nonlinear interior dissipation (2006, background): “5] for similar estimates for von Karman equations (see also [7]).”
Strongly damped wave problems: Bootstrapping and regularity of solutions (2008, background): “For example, if ∆D denotes the Dirichlet Laplacian in a bounded smooth domain Ω ⊂ R, θ = 1 and D = A = −∆D, M = I, H = L(Ω), f : R→ R and F (u, ut)(x) = f(u(x)), the growth that we obtain for f is 5, whereas in [13] it is 3.”
Long-time Behavior of Second Order Evolution Equations With Nonlinear Damping (2008, methodology): “For applications of this method we also refer to [27, 89] in the case of wave dynamics with interior dissipation, to [22, 26] for wave and plate systems with boundary damping, and to the paper [34] which involves the same idea in the study metric properties of trajectory attractors.”
Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping (2007, methodology): “5 are known for the case of pure interior damping d = 0, d0 > 0 [13], where d0 is assumed sufficiently large.”
Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R^3 (2008, background): “Particularly, the existence of these attractors was proved in [2, 3, 4, 11, 18, 22, 32, 33] for the deterministic equation defined in bounded domains with critical exponents, and in [16, 17, 27, 28, 29] for the equation defined on unbounded domains with critical or supercritical exponents.”
Asymptotic behavior of stochastic wave equations with critical exponents on $\mathbb{R}^{3}$ (2008, background): “Particularly, the existence of these attractors was proved in [2, 3, 4, 11, 18, 22, 32, 33] for the deterministic equation defined in bounded domains with critical exponents, and in [16, 17, 27, 28, 29] for the equation defined on unbounded domains with critical or supercritical exponents.”