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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 specic integral inequality to prove that the solution decays exponentially to zero when the time t goes to innit y.

Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping