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

Research output: Contribution to journalArticle

1 Citation (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 languageEnglish
Pages (from-to)63-82
Number of pages20
JournalKyushu Journal of Mathematics
Volume70
Issue number1
DOIs
Publication statusPublished - 2016
Externally publishedYes

Fingerprint

Difference Inequalities
Quasilinear Wave Equation
Kelvin
P-Laplacian
Global Solution
Initial-boundary-value Problem
Dissipation
Nonlinearity
Derivative
Energy
Estimate

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

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KW - Kelvin-Voigt dissipation

KW - P-Laplacian

KW - Quasilinear wave equation

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