Large time behavior of solutions for a system of nonlinear damped wave equations

Takayoshi Ogawa, Hiroshi Takeda

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We consider the Cauchy problem of the semilinear damped wave system: {∂t2u -Δu +∂tu=F(u), t>0, x ∈ R{double-struck}n, uj (0, x) =aj(x), ∂t uj (0, x) =bj (x), x ∈ R{double-struck}n, where u(t,x)=(u1(t,x),...,um(t,x)) with m≥2 and j=1,...,m. We show the asymptotic behavior of solutions under the sharp condition on the nonlinear exponents, which is a natural extension of the results for the single nonlinear damped wave equations Nishihara (2003) [21], Hayashi et al. (2004) [9], Hosono and Ogawa (2004) [10]. The proof is based on the Lp- Lq type decomposition of the fundamental solutions of the linear damped wave equations into the dissipative part and hyperbolic part Hosono and Ogawa (2004) [10], Nishihara (2003) [21].

Original languageEnglish
Pages (from-to)3090-3113
Number of pages24
JournalJournal of Differential Equations
Volume251
Issue number11
DOIs
Publication statusPublished - 2011 Dec 1

Keywords

  • Asymptotic profile
  • Critical exponent
  • Global solution
  • Large time behavior
  • Nonlinear damped wave equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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