Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation. (7th April 2014)

• Record Type: Journal Article
• Authors: Kim, Daewook; Kim, Dojin; Hong, Keum-Shik; Jung, Il Hyo
• Other Names: Baleanu D. Academic Editor.; Jafari H. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-04-07
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/716740
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : 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 K u ′ ′ + M A 1 / 2 u 2 A u + 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.