Existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity

Mitsuhiro Nakao

doi:10.1016/j.jde.2013.07.060

Existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity

Mitsuhiro Nakao^*

^*Corresponding author for this work

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

11 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	3940-3970
Number of pages	31
Journal	Journal of Differential Equations
Volume	255
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2013.07.060
Publication status	Published - 2013 Dec 1
Externally published	Yes

Keywords

Derivative nonlinearity
Energy decay
Global solutions
Klein-Gordon equation
Nonlinear dissipation

ASJC Scopus subject areas

Analysis

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10.1016/j.jde.2013.07.060

Cite this

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title = "Existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity",

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

keywords = "Derivative nonlinearity, Energy decay, Global solutions, Klein-Gordon equation, Nonlinear dissipation",

author = "Mitsuhiro Nakao",

year = "2013",

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N2 - We prove the existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity. To derive the required estimates of solutions we employ a 'loan' method.

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

KW - Derivative nonlinearity

KW - Energy decay

KW - Global solutions

KW - Klein-Gordon equation

KW - Nonlinear dissipation

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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ER -

Existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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