Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku′′ + M(|A (1/2) u|(2))Au + g(u′) = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the e...

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Detalles Bibliográficos
Autores principales: Kim, Daewook, Kim, Dojin, Hong, Keum-Shik, Jung, Il Hyo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3996994/
https://www.ncbi.nlm.nih.gov/pubmed/24977217
http://dx.doi.org/10.1155/2014/716740
Descripción
Sumario:The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku′′ + M(|A (1/2) u|(2))Au + g(u′) = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.

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