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
Mitsuhiro Nakao
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.
About the authors ▼
Mitsuhiro Nakao
Kyushu University, Faculty of Mathematics, Moto-oka, Fukuoka 819-0395, Japan
About the article ▼
Received: 2014-02-14.
Revised: 2014-03-03.
Accepted: 2014-03-03.
Cite this article as ▼
Mitsuhiro Nakao, Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity, Opuscula Math. 34, no. 3 (2014), 569-590,
http://dx.doi.org/10.7494/OpMath.2014.34.3.569.
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