Strong attractors for the strongly damped wave equations on time-dependent spaces
نویسندگان
چکیده
We examine the long-term behavior of strong solutions for wave equation $ \varepsilon(t)u_{tt}-\Delta u_{t}-\Delta u+f(u) = g(x) and obtain time-dependent attractor in \mathcal{H}_{t}^{1} [H^{2}(\Omega)\cap H_{0}^{1}(\Omega)]\times H_{0}^{1}(\Omega) $. Moreover, is bounded H_{0}^{1}(\Omega)]\times[H^{2}(\Omega)\cap H_{0}^{1}(\Omega)]
منابع مشابه
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...
متن کاملUniform 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...
متن کاملGlobal Attractors for Damped Semilinear Wave Equations
The existence of a global attractor in the natural energy space is proved for the semilinear wave equation utt + βut − ∆u + f(u) = 0 on a bounded domain Ω ⊂ R with Dirichlet boundary conditions. The nonlinear term f is supposed to satisfy an exponential growth condition for n = 2, and for n ≥ 3 the growth condition |f(u)| ≤ c0(|u|γ + 1), where 1 ≤ γ ≤ n n−2 . No Lipschitz condition on f is assu...
متن کاملUpper semicontinuity of attractors for the discretization of strongly damped wave equations
In most problems, the ideal situation is having the asymptotic dynamics of one equation the same as the asymptotic dynamics of its discretization. Although, when we are studying the linear wave equation, we note that the spectrum of discretization and the spectrum of its continuous counterpart are far away from each other, no matter how fine the discretization is. This fact is restrictive in th...
متن کاملAttractors for Stochastic Strongly Damped Plate Equations with Additive Noise
We study the asymptotic behavior of stochastic plate equations with homogeneous Neumann boundary conditions. We show the existence of an attractor for the random dynamical system associated with the equation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems-series B
سال: 2023
ISSN: ['1531-3492', '1553-524X']
DOI: https://doi.org/10.3934/dcdsb.2022207