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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article number123455
JournalJournal of Mathematical Analysis and Applications
Volume481
Issue number1
DOIs
Publication statusPublished - 2020 Jan 1

Fingerprint

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

Keywords

  • Critical Besov spaces
  • Generalized double dispersion equation
  • Global existence
  • Optimal decay estimates

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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abstract = "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.",
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AU - Wang, Yuzhu

AU - Xu, Jiang

AU - Kawashima, Shuichi

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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.

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KW - Generalized double dispersion equation

KW - Global existence

KW - Optimal decay estimates

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