On global smooth solutions to the initial-boundary value problem for quasilinear wave equations in exterior domains

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概要

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• We consider the initial-boundary value problem for the standard quasi-linear wave equation: u<SUB>tt</SUB>-div{σ(|∇<SUB>u</SUB>|<SUP>2</SUP>)∇<SUB>u</SUB>}+a(x)u<SUB>t</SUB>=0 in Ω×[0, ∞) u(x, 0)=u<SUB>0</SUB>(x) and u<SUB>t</SUB>(x, 0)=u<SUB>1</SUB>(x) and u|<SUB>∂Ω</SUB>=0 where Ω is an exterior domain in R<SUP>N</SUP>, σ(v) is a function like σ(v)=1/√{1+v} and a(x) is a nonnegative function. Under two types of hypotheses on a(x) we prove existence theorems of global small amplitude solutions. We note that a(x)u<SUB>t</SUB> is required to be effective only in localized area and no geometrical condition is imposed on the boundary ∂Ω.

• 社団法人 日本数学会の論文
• 2003-07-01

著者

• NAKAO Mitsuhiro

  Graduate School of Mathematics Kyushu University

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