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

M. Aassila, Université Louis Pasteur et C.N.R.S., Strasbourg Cédex, France

E. J. Qualitative Theory of Diff. Equ., No. 7. (1998), pp. 1-12.

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.

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