Electronic Journal of Qualitative Theory of Differential Equations (Jan 1998)
Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping
Abstract
We prove the existence and uniqueness of a global solution of a damped quasilinear hyperbolic equation. Key point to our proof is the use of the Yosida approximation. Furthermore, we apply a method based on a specific integral inequality to prove that the solution decays exponentially to zero when the time t goes to infinity.