Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain

Nakao Hayashi

doi:10.1007/BF02567842

Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain

Nakao Hayashi

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study the initial boundary value problem for the nonlinear wave equation: {Mathematical expression} where n=4,5, u₀, u₁ are real valued functions and ∈₀ is a sufficiently small positive constant. In this paper we shall show small solutions to (*) exist globally in time under the condition that the nonlinear term F:ℝ²→ℝ is quadratic with respect to ∂_t u and ∂_t² u.

Original language	English
Pages (from-to)	15-39
Number of pages	25
Journal	Manuscripta Mathematica
Volume	81
Issue number	1
DOIs	https://doi.org/10.1007/BF02567842
Publication status	Published - 1993 Dec

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abstract = "We study the initial boundary value problem for the nonlinear wave equation: {Mathematical expression} where n=4,5, u 0, u 1 are real valued functions and ∈0 is a sufficiently small positive constant. In this paper we shall show small solutions to (*) exist globally in time under the condition that the nonlinear term F:ℝ2→ℝ is quadratic with respect to ∂ t u and ∂ t 2 u.",

author = "Nakao Hayashi",

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AB - We study the initial boundary value problem for the nonlinear wave equation: {Mathematical expression} where n=4,5, u 0, u 1 are real valued functions and ∈0 is a sufficiently small positive constant. In this paper we shall show small solutions to (*) exist globally in time under the condition that the nonlinear term F:ℝ2→ℝ is quadratic with respect to ∂ t u and ∂ t 2 u.

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Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain

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