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Strongly damped wave equation in uniform spaces

โœ Scribed by J.W. Cholewa; Tomasz Dlotko

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
174 KB
Volume
64
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

The Cauchy problem for a semilinear strongly damped wave equation is considered in the whole of R n . Under suitable conditions imposed on nonlinear term, which are much like for equations in bounded domains, a dissipative semigroup {T(t)} of global solutions to this problem is constructed in a reach phase space being the product of the locally uniform spaces. Existence of an attractor for {T(t)} is then established.

๐Ÿ“œ SIMILAR VOLUMES

Partition of energy in strongly damped g
Partition of energy in strongly damped generalized wave equations
โœ Piotr Biler ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 430 KB

## Abstract Dissipative perturbations of hyperbolic equations such as __u__~__tt__~ + __Bu__~__t__~ + __A__^2^__u__ = 0 with positive operators __A__, __B__ are considered. The rates of decay and partition of energy theorems are established for solutions of these equations.

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The existence and estimate of the upper bound of the Hausdorff dimension of the global attractor for the strongly damped nonlinear wave equation with the Dirichlet boundary condition are considered by introducing a new norm in the phase space. The gained Hausdorff dimension decreases as the damping