Global existence and decay for nonlinear dissipative wave equations with a derivative nonlinearity

Mitsuhiro Nakao

doi:10.1016/j.na.2011.10.022

Global existence and decay for nonlinear dissipative wave equations with a derivative nonlinearity

Mitsuhiro Nakao^*

^*Corresponding author for this work

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

8 Citations (Scopus)

Abstract

We prove the global existence of the so-called ^H2 solutions for a nonlinear wave equation with a nonlinear dissipative term and a derivative type nonlinear perturbation. To show the boundedness of the second order derivatives we need a precise energy decay estimate and for this we employ a 'loan' method.

Original language	English
Pages (from-to)	2236-2248
Number of pages	13
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	75
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2011.10.022
Publication status	Published - 2012 Mar
Externally published	Yes

Keywords

Energy decay
Global existence
Nonlinear dissipation
Nonlinear wave equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2011.10.022

Cite this

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title = "Global existence and decay for nonlinear dissipative wave equations with a derivative nonlinearity",

abstract = "We prove the global existence of the so-called H2 solutions for a nonlinear wave equation with a nonlinear dissipative term and a derivative type nonlinear perturbation. To show the boundedness of the second order derivatives we need a precise energy decay estimate and for this we employ a 'loan' method.",

keywords = "Energy decay, Global existence, Nonlinear dissipation, Nonlinear wave equation",

author = "Mitsuhiro Nakao",

year = "2012",

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doi = "10.1016/j.na.2011.10.022",

language = "English",

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AU - Nakao, Mitsuhiro

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AB - We prove the global existence of the so-called H2 solutions for a nonlinear wave equation with a nonlinear dissipative term and a derivative type nonlinear perturbation. To show the boundedness of the second order derivatives we need a precise energy decay estimate and for this we employ a 'loan' method.

KW - Energy decay

KW - Global existence

KW - Nonlinear dissipation

KW - Nonlinear wave equation

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M3 - Article

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SN - 0362-546X

VL - 75

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EP - 2248

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 4

ER -

Global existence and decay for nonlinear dissipative wave equations with a derivative nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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