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Algebra and Geometry Through Hamiltonian Systems Read chapter Read first chapter

2014 | OriginalPaper | Chapter

16. On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity

Authors : Nataliia V. Gorban, Oleksiy V. Kapustyan, Pavlo O. Kasyanov, Liliia S. Paliichuk

Published in: Continuous and Distributed Systems

Publisher: Springer International Publishing

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Abstract

We consider autonomous damped wave equation with discontinuous nonlinearity. The long-term prognosis of the state functions when the conditions on the parameters of the problem do not guarantee uniqueness of solution of the corresponding Cauchy problem are studied. We prove the existence of a global attractor and investigate its structure. It is obtained that trajectory of every weak solution defined on \([0;+\infty )\) tends to a fixed point.

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previous chapter On Regularity of All Weak Solutions and Their Attractors for Reaction-Diffusion Inclusion in Unbounded Domain
next chapter On the Regularities of Mass Random Phenomena
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Metadata
Title
On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity
Authors
Nataliia V. Gorban
Oleksiy V. Kapustyan
Pavlo O. Kasyanov
Liliia S. Paliichuk
Copyright Year
2014
Book
Continuous and Distributed Systems

Print ISBN: 978-3-319-03145-3

Electronic ISBN: 978-3-319-03146-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-03146-0_16