Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type

Hiromichi Hashimoto, Taeko Yamazaki

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We consider a hyperbolic-parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic-parabolic singular perturbation problem for linear equations with a time-dependent coefficient.

Original languageEnglish
Pages (from-to)491-525
Number of pages35
JournalJournal of Differential Equations
Volume237
Issue number2
DOIs
Publication statusPublished - 15 Jun 2007

Keywords

  • Dissipative hyperbolic equation
  • Kirchhoff equation
  • Quasilinear equation
  • Singular perturbation problem

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