Pullback attractors for a critical degenerate wave equation with time-dependent damping
نویسندگان
چکیده
The aim of this paper is to analyze the long-time dynamical behavior solution for a degenerate wave equation with time-dependent damping term ∂ t u + β ( ) = L x , f on bounded domain Ω ⊂ R N Dirichlet boundary conditions. Under some restrictions and critical growth nonlinear we will prove local global well-posedness derive existence pullback attractor process associated damped hyperbolic problem.
منابع مشابه
Critical Exponent for a Nonlinear Wave Equation with Damping
It is well known that if the damping is missing, the critical exponent for the nonlinear wave equation gu=|u| p is the positive root p0(n) of the equation (n&1) p&(n+1) p&2=0, where n 2 is the space dimension (for p0(1)= , see Sideris [14]). The proof of this fact, known as Strauss' conjecture [17], took more than 20 years of effort, beginning with Glassey doi:10.1006 jdeq.2000.3933, available ...
متن کاملSmooth attractors for the quintic wave equations with fractional damping
Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors...
متن کاملRegularity and Scattering for the Wave Equation with a Critical Nonlinear Damping
We show that the nonlinear wave equation u + ut = 0 is globally well-posed in radially symmetric Sobolev spaces Hk rad(R 3) × Hk−1 rad (R 3) for all integers k > 2. This partially extends the well-posedness in Hk(R3) × Hk−1(R3) for all k ∈ [1, 2], established by Lions and Strauss [12]. As a consequence we obtain the global existence of C∞ solutions with radial C∞ 0 data. The regularity problem ...
متن کاملBi-space pullback attractors for closed processes
In the description of the long-time behavior of solutions to nonautonomous differential equations the notion of a pullback attractor plays a similar role as the global attractor in autonomous dynamical systems. We present the theorem on the existence of a pullback attractor if the evolution process is a family of closed operators. The abstract result is formulated in the context of the smoothin...
متن کاملDamping for the elastic wave equation
Résumé: Le but de ce projet est une investigation des techniques d’amortissement pour l’équation d’onde. Cette étude est intéressante tant du point de vue de la physique et que de l’analyse numérique. En effet l’amortissement apparâıt fréquemment dans les systèmes avec friction. Du point de vue mathématique, l’amortissement donne une meilleure régularité de l’équation élastique qui est importan...
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: Nonlinear Analysis-real World Applications
سال: 2022
ISSN: ['1878-5719', '1468-1218']
DOI: https://doi.org/10.1016/j.nonrwa.2021.103421