Existence of global decaying solutions to the initial boundary value problem for quasilinear viscoelastic equations of p-Laplacian type with a derivative nonlinearity

Mitsuhiro Nakao

doi:10.2206/kyushujm.70.63

Existence of global decaying solutions to the initial boundary value problem for quasilinear viscoelastic equations of p-Laplacian type with a derivative nonlinearity

Mitsuhiro Nakao^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We prove the existence of global decaying solutions to the initial boundary value problem for the quasilinear wave equation of p-Laplacian type with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a ‘loan’ method and a difference inequality for the energy.

Original language	English
Pages (from-to)	63-82
Number of pages	20
Journal	Kyushu Journal of Mathematics
Volume	70
Issue number	1
DOIs	https://doi.org/10.2206/kyushujm.70.63
Publication status	Published - 2016
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

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10.2206/kyushujm.70.63

Cite this

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title = "Existence of global decaying solutions to the initial boundary value problem for quasilinear viscoelastic equations of p-Laplacian type with a derivative nonlinearity",

abstract = "We prove the existence of global decaying solutions to the initial boundary value problem for the quasilinear wave equation of p-Laplacian type with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a {\textquoteleft}loan{\textquoteright} method and a difference inequality for the energy.",

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

author = "Mitsuhiro Nakao",

year = "2016",

doi = "10.2206/kyushujm.70.63",

language = "English",

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journal = "Kyushu Journal of Mathematics",

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publisher = "Kyushu University, Faculty of Science",

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AU - Nakao, Mitsuhiro

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N2 - We prove the existence of global decaying solutions to the initial boundary value problem for the quasilinear wave equation of p-Laplacian type with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a ‘loan’ method and a difference inequality for the energy.

AB - We prove the existence of global decaying solutions to the initial boundary value problem for the quasilinear wave equation of p-Laplacian type with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a ‘loan’ method and a difference inequality for the energy.

KW - Derivative nonlinearity

KW - Energy decay

KW - Global solutions

KW - Kelvin-Voigt dissipation

KW - P-Laplacian

KW - Quasilinear wave equation

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Existence of global decaying solutions to the initial boundary value problem for quasilinear viscoelastic equations of p-Laplacian type with a derivative nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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