Opuscula Math. 34, no. 3 (2014), 569-590
http://dx.doi.org/10.7494/OpMath.2014.34.3.569

 
Opuscula Mathematica

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.

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  • Mitsuhiro Nakao
  • Kyushu University, Faculty of Mathematics, Moto-oka, Fukuoka 819-0395, Japan
  • Received: 2014-02-14.
  • Revised: 2014-03-03.
  • Accepted: 2014-03-03.
Opuscula Mathematica - cover

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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