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

Mitsuhiro Nakao

Research output: Contribution to journalArticle

5 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 languageEnglish
Pages (from-to)569-590
Number of pages22
JournalOpuscula Mathematica
Volume34
Issue number3
DOIs
Publication statusPublished - 2014
Externally publishedYes

Fingerprint

Difference Inequalities
Quasilinear Wave Equation
Kelvin
Global Solution
Initial-boundary-value Problem
Dissipation
Existence and Uniqueness
Nonlinearity
Derivative
Energy
Estimate

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity. / Nakao, Mitsuhiro.

In: Opuscula Mathematica, Vol. 34, No. 3, 2014, p. 569-590.

Research output: Contribution to journalArticle

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