Global Existence of Small Solutions to Quadratic Nonlinear Wave Equations in an Exterior Domain

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13 Citations (Scopus)

Abstract

We consider the initial boundary value problem for the nonlinear wave equation [formula] where □ = ∂2t − ΔB = (x : |x| = [formula] > R), ∂B = (x : |x| = R), u0, u1 are real valued functions ϵ0 is a sufficiently small positive constant. In this paper it is shown that small solutions to (*) exist globally in time when n = 4. Our method in this paper is applicable to the more general nonlinear wave equations such that □u = F(∂tu, ∂t ∂u, ∂2tu), where F is a quadratic nonlinearity in (∂tu, part;t ∂u, ∂2tu), ∂ = (∂1, ∂2, … , ∂n) and n ≥ 4.

Original languageEnglish
Pages (from-to)302-344
Number of pages43
JournalJournal of Functional Analysis
Volume131
Issue number2
DOIs
Publication statusPublished - 1995 Aug 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis

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