Asymptotic profile of solutions to nonlinear dissipative evolution system with ellipticity

Kenji Nishihara

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We consider the Cauchy problem for the nonlinear dissipative evolution system with ellipticity on one dimensional space equation presented, with 0 < ν2 < 4 α (1 - α), 0 < α < 1. S. Q. Tang and H. Zhao [4] have considered the problem and obtained the optimal decay property for suitably small data. In this paper we derive the asymptotic profile using the Gauss kernel G(t, x), which shows the precise behavior of solution as time tends to infinity. In fact, we will show that the asymptotic formula equation presented, holds, where D 0, β0 are determined by the data. It is the key point to reformulate the system to the nonlinear parabolic one by suitable changing variables.

Original languageEnglish
Pages (from-to)604-614
Number of pages11
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume57
Issue number4
DOIs
Publication statusPublished - 2006 Jul
Externally publishedYes

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Keywords

  • Asymptotic profile
  • Evolution system with ellipticity
  • Parabolic system

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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