We consider a one-dimensional weakly damped wave equation, with a damping coefficient depending on the displacement. We prove the existence of a regular connected global attractor of finite fractal dimension for the associated dynamical system, as well as the existence of an exponential attractor.
A one-dimensional wave equation with nonlinear damping / Gatti, Stefania; Pata, V.. - In: GLASGOW MATHEMATICAL JOURNAL. - ISSN 0017-0895. - STAMPA. - 48:3(2006), pp. 419-430. [10.1017/S0017089506003156]
A one-dimensional wave equation with nonlinear damping
GATTI, Stefania;
2006
Abstract
We consider a one-dimensional weakly damped wave equation, with a damping coefficient depending on the displacement. We prove the existence of a regular connected global attractor of finite fractal dimension for the associated dynamical system, as well as the existence of an exponential attractor.
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