title: Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation.
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 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.
authors: Department of Mathematics, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea.
authors: Daewook
authors: 0000-0002-7929-1343
authors: D
authors: Kim
authors: Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA.
authors: Dojin
authors: D
authors: Kim
authors: Department of Cogno-Mechatronics Engineering and School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea.
authors: Keum-Shik
authors: KS
authors: Hong
authors: Department of Mathematics, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea.
authors: Il Hyo
authors: IH
authors: Jung
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004735:Energy Transfer; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*