Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

Mitsuhiro Nakao

doi:10.7494/OpMath.2014.34.3.569

Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

Mitsuhiro Nakao^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	569-590
Number of pages	22
Journal	Opuscula Mathematica
Volume	34
Issue number	3
DOIs	https://doi.org/10.7494/OpMath.2014.34.3.569
Publication status	Published - 2014
Externally published	Yes

Keywords

Derivative nonlinearity
Energy decay
Global solutions
Kelvin-Voigt dissipation
Quasilinear wave equation

ASJC Scopus subject areas

Mathematics(all)

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10.7494/OpMath.2014.34.3.569

Cite this

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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 = "Derivative nonlinearity, Energy decay, Global solutions, Kelvin-Voigt dissipation, Quasilinear wave equation",

author = "Mitsuhiro Nakao",

year = "2014",

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AB - 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.

KW - Derivative nonlinearity

KW - Energy decay

KW - Global solutions

KW - Kelvin-Voigt dissipation

KW - Quasilinear wave equation

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Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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