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Attractors for damped quintic wave equations in bounded domains
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In this article, the existence of a compact global attractor for the solution semigroup of the dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered.Abstract:
The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.read more
Citations
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Journal ArticleDOI
Pullback Attractors for a Damped Semilinear Wave Equation with Delays
TL;DR: In this paper, the authors considered weakly damped wave equations with hereditary effects and verified the existence of the pullback D-attractor in the energy functional and the contractive function.
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Continuity of non-autonomous attractors for hyperbolic perturbation of parabolic equations
TL;DR: In this paper, the lower and upper semicontinuity of pullback, uniform, and cocycle attractors for the non-autonomous dynamical system given by hyperbolic equation on a bounded domain was proved.
Lectures On Non-Linear Wave Equations, Second Edition By Christopher D. Sogge (Johns Hopkins University)
TL;DR: Sogge as mentioned in this paper presented an account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear Lectures on NonLinear Wave Equations (Englisch) Fremdsprachige B cher Lectures, Second Lectures On Nonlinear Wave Equation, Second Edition Christopher D. Sogge.
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Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains
TL;DR: In this paper, Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form $(-\Delta)^\alpha\partial_t u$, $\alpha\in(0,\frac{1}{2})$, in bounded smooth domains of $\Bbb R^3".
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Smooth attractors for the quintic wave equations with fractional damping
Anton Savostianov,Sergey Zelik +1 more
TL;DR: 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 of finite Hausdorff and fractal dimension is verified.
References
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TL;DR: In this article, the authors consider a continuous dynamical system with a global attractor and describe the properties of the flow on the attractor asymptotically smooth and Morse-Smale maps.
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