Opuscula Math. 34, no. 3 (2014), 569-590
Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity
Abstract. We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.
Keywords: global solutions, energy decay, quasilinear wave equation, Kelvin-Voigt dissipation, derivative nonlinearity.
Mathematics Subject Classification: 35B35, 35B40, 35L70.