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 journalArticle

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 languageEnglish
Pages (from-to)457-477
Number of pages21
JournalFunkcialaj Ekvacioj
Volume55
Issue number3
DOIs
Publication statusPublished - 2012
Externally publishedYes

Fingerprint

Nonlinear Dissipation
Dissipative Equations
Global Solution
Wave equation
Cauchy Problem
Nonlinearity
Derivative
Estimate

Keywords

  • Derivative nonlinearity
  • Energy decay
  • Global solutions
  • Nonlinear dissipation
  • Wave equation

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

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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 - Energy decay

KW - Global solutions

KW - Nonlinear dissipation

KW - Wave equation

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