Global existence and optimal time-decay estimates of solutions to the generalized double dispersion equation on the framework of Besov spaces

Yuzhu Wang, Jiang Xu, Shuichi Kawashima

研究成果: Article

抄録

We investigate the initial value problem for the generalized double dispersion equation in any dimensions. Inspired by [28] for the hyperbolic system of first order PDEs, we develop Littlewood-Paley pointwise energy estimates for the dissipative wave equation of high-order. Furthermore, with aid of the frequency-localization Duhamel principle, we establish the global existence and optimal decay estimates of solutions in spatially critical Besov spaces. Our results could hold true for any dimensions (n≥1). Indeed, the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks.

元の言語English
記事番号123455
ジャーナルJournal of Mathematical Analysis and Applications
481
発行部数1
DOI
出版物ステータスPublished - 2020 1 1

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Decay Estimates
Initial value problems
Besov Spaces
Wave equations
Global Existence
Interpolation
Dissipative Equations
Pointwise Estimates
Energy Estimates
Hyperbolic Systems
Higher Dimensions
Initial Value Problem
Wave equation
Interpolate
Higher Order
First-order
Framework

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

これを引用

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T1 - Global existence and optimal time-decay estimates of solutions to the generalized double dispersion equation on the framework of Besov spaces

AU - Wang, Yuzhu

AU - Xu, Jiang

AU - Kawashima, Shuichi

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We investigate the initial value problem for the generalized double dispersion equation in any dimensions. Inspired by [28] for the hyperbolic system of first order PDEs, we develop Littlewood-Paley pointwise energy estimates for the dissipative wave equation of high-order. Furthermore, with aid of the frequency-localization Duhamel principle, we establish the global existence and optimal decay estimates of solutions in spatially critical Besov spaces. Our results could hold true for any dimensions (n≥1). Indeed, the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks.

AB - We investigate the initial value problem for the generalized double dispersion equation in any dimensions. Inspired by [28] for the hyperbolic system of first order PDEs, we develop Littlewood-Paley pointwise energy estimates for the dissipative wave equation of high-order. Furthermore, with aid of the frequency-localization Duhamel principle, we establish the global existence and optimal decay estimates of solutions in spatially critical Besov spaces. Our results could hold true for any dimensions (n≥1). Indeed, the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks.

KW - Critical Besov spaces

KW - Generalized double dispersion equation

KW - Global existence

KW - Optimal decay estimates

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