On the critical nonlinear damped wave equation with large initial data

Nakao Hayashi, Elena I. Kaikina, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

We study the nonlinear damped wave equation(0.1){(ut t + ut - Δ u = - | u |σ u, x ∈ Rn, t > 0,; u (0, x) = u0 (x), ut (0, x) = u1 (x), x ∈ Rn,) in the critical case of σ = frac(2, n). Our aim is to prove the large time asymptotic formulas for solutions of the Cauchy problem (0.1) without any restriction on the size of the initial data and on the spatial dimension.

Original languageEnglish
Pages (from-to)1400-1425
Number of pages26
JournalJournal of Mathematical Analysis and Applications
Volume334
Issue number2
DOIs
Publication statusPublished - 2007 Oct 15
Externally publishedYes

Keywords

  • Asymptotic formulas
  • Critical nonlinearity
  • Dissipative wave equations
  • Large data

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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