Existence of global decaying solutions to the Cauchy problem for a nonlinear dissipative wave equation of Klein-Gordon type with a derivative nonlinearity

Mitsuhiro Nakao

doi:10.1619/fesi.55.457

Existence of global decaying solutions to the Cauchy problem for a nonlinear dissipative wave equation of Klein-Gordon type with a derivative nonlinearity

Mitsuhiro Nakao

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

2 Citations (Scopus)

Abstract

We prove the existence of global decaying solutions to the Cauchy problem for the wave equation of Klein-Gordon type with a nonlinear dissipation and a derivative nonlinearity. To derive required estimates of solutions we employ a delicate 'loan' method.

Original language	English
Pages (from-to)	457-477
Number of pages	21
Journal	Funkcialaj Ekvacioj
Volume	55
Issue number	3
DOIs	https://doi.org/10.1619/fesi.55.457
Publication status	Published - 2012
Externally published	Yes

Keywords

Derivative nonlinearity
Energy decay
Global solutions
Nonlinear dissipation
Wave equation

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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abstract = "We prove the existence of global decaying solutions to the Cauchy problem for the wave equation of Klein-Gordon type with a nonlinear dissipation and a derivative nonlinearity. To derive required estimates of solutions we employ a delicate 'loan' method.",

keywords = "Derivative nonlinearity, Energy decay, Global solutions, Nonlinear dissipation, Wave equation",

author = "Mitsuhiro Nakao",

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KW - Derivative nonlinearity

KW - Energy decay

KW - Global solutions

KW - Nonlinear dissipation

KW - Wave equation

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Existence of global decaying solutions to the Cauchy problem for a nonlinear dissipative wave equation of Klein-Gordon type with a derivative nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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