Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation. (7th April 2014) - Kim, Daewook; Kim, Dojin; Hong, Keum-Shik; Jung, Il Hyo
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.