Asymptotic Periodicity for Strongly Damped Wave Equations

Attractors for Strongly Damped Wave Equations with Critical Nonlinearities

In this paper we obtain global well-posedness results for the strongly damped wave equation utt + (−∆)θut = ∆u + f(u), for θ ∈ [1 2 , 1 ] , in H 0(Ω)×L(Ω) when Ω is a bounded smooth domain and the map f grows like |u|n+2 n−2 . If f = 0, then this equation generates an analytic semigroup with generator −A(θ). Special attention is devoted to the case when θ = 1 since in this case the generator −A...

Uniform Exponential Attractors for Non-Autonomous Strongly Damped Wave Equations

In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform Hölder continuity is established to the variation of the process in the phase apace. In a certain parameter region, the exponential attractor is a uniformly exponentially attracting time-dependent set in the phase apace, and is finite-d...

Asymptotic Expansion for Damped Wave Equations with Periodic Coefficients

Asymptotic behaviour of strongly damped nonlinear hyperbolic equations

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A Variational Approach to Strongly Damped Wave Equations

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix–Haase, thus extending several known results and obtaining optimal analyticity angle.