Decay rates of solutions to dissipative nonlinear evolution equations with ellipticity

Changjiang Zhu, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)

Abstract

In this paper, we study the global existence and the asymptotic behavior of the solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects with initial data (ψ, θ)(x, 0) = (ψ0(x),θ0(x)) → (ψ±, θ±) as → ±∞, (I) where α and νare positive constants such that α < 1, ν < α(1 - α). Through constructing a correct function θ(x, t) defined by (2.13) and using the energy method, we show sup(|(ψ, θ)(x, t)|+ |(ψx, θx)(x, t)|) → 0 as t → ∞ and the solutions decay with exponential rates. The same problem is studied by Tang and Zhao [10] for the case of (ψ±, θ±) = (0, 0).
Original languageEnglish
Pages (from-to)994-1014
Number of pages21
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume55
Issue number6
DOIs
Publication statusPublished - 1 Nov 2004
Externally publishedYes

Keywords

  • a priori estimates
  • Correct function
  • Decay rates
  • Energy method

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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