Nonlinear dispersive wave equations in two space dimensions

Nakao Hayashi; Seishirou Kobayashi; Pavel I. Naumkin

doi:10.3934/cpaa.2015.14.1377

Nonlinear dispersive wave equations in two space dimensions

Nakao Hayashi, Seishirou Kobayashi, Pavel I. Naumkin

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

Abstract

We study the global existence and time decay of solutions to nonlinear dispersive wave equations ∂² _t u + 1/ρ²(-Δ)ρ u = F (∂tu) in two space dimensions, where F (∂tu) = λ∂tu^p-1∂tu or λ∂tu^p-, λ∈ C; with p > 2 for 0 < ρ < 1; p > 3 for ρ = 1; and p > 1 + ρ for 1 < ρ < 2: If ρ = 1; then the equation converts into the well-known nonlinear wave equation.

Original language	English
Pages (from-to)	1377-1393
Number of pages	17
Journal	Communications on Pure and Applied Analysis
Volume	14
Issue number	4
DOIs	https://doi.org/10.3934/cpaa.2015.14.1377
Publication status	Published - 2015 Jul 1
Externally published	Yes

Keywords

Asymptotic behavior
Dispersive nonlinear wave
Global in time of solutions
System of equations
Vector field method

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2015.14.1377

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title = "Nonlinear dispersive wave equations in two space dimensions",

abstract = "We study the global existence and time decay of solutions to nonlinear dispersive wave equations ∂2 t u + 1/ρ2(-Δ)ρ u = F (∂tu) in two space dimensions, where F (∂tu) = λ∂tup-1∂tu or λ∂tup-, λ∈ C; with p > 2 for 0 < ρ < 1; p > 3 for ρ = 1; and p > 1 + ρ for 1 < ρ < 2: If ρ = 1; then the equation converts into the well-known nonlinear wave equation.",

keywords = "Asymptotic behavior, Dispersive nonlinear wave, Global in time of solutions, System of equations, Vector field method",

author = "Nakao Hayashi and Seishirou Kobayashi and Naumkin, {Pavel I.}",

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T1 - Nonlinear dispersive wave equations in two space dimensions

AU - Hayashi, Nakao

AU - Kobayashi, Seishirou

AU - Naumkin, Pavel I.

PY - 2015/7/1

Y1 - 2015/7/1

N2 - We study the global existence and time decay of solutions to nonlinear dispersive wave equations ∂2 t u + 1/ρ2(-Δ)ρ u = F (∂tu) in two space dimensions, where F (∂tu) = λ∂tup-1∂tu or λ∂tup-, λ∈ C; with p > 2 for 0 < ρ < 1; p > 3 for ρ = 1; and p > 1 + ρ for 1 < ρ < 2: If ρ = 1; then the equation converts into the well-known nonlinear wave equation.

AB - We study the global existence and time decay of solutions to nonlinear dispersive wave equations ∂2 t u + 1/ρ2(-Δ)ρ u = F (∂tu) in two space dimensions, where F (∂tu) = λ∂tup-1∂tu or λ∂tup-, λ∈ C; with p > 2 for 0 < ρ < 1; p > 3 for ρ = 1; and p > 1 + ρ for 1 < ρ < 2: If ρ = 1; then the equation converts into the well-known nonlinear wave equation.

KW - Asymptotic behavior

KW - Dispersive nonlinear wave

KW - Global in time of solutions

KW - System of equations

KW - Vector field method

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JO - Communications on Pure and Applied Analysis

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SN - 1534-0392

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Nonlinear dispersive wave equations in two space dimensions

Abstract

Keywords

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