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 language | English |
|---|---|
| Article number | 123455 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 481 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2020 Jan 1 |
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Keywords
- Critical Besov spaces
- Generalized double dispersion equation
- Global existence
- Optimal decay estimates
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Global existence and optimal time-decay estimates of solutions to the generalized double dispersion equation on the framework of Besov spaces. / Wang, Yuzhu; Xu, Jiang; Kawashima, Shuichi.
In: Journal of Mathematical Analysis and Applications, Vol. 481, No. 1, 123455, 01.01.2020.Research output: Contribution to journal › Article
}
TY - JOUR
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
UR - http://www.scopus.com/inward/record.url?scp=85071611116&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85071611116&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2019.123455
DO - 10.1016/j.jmaa.2019.123455
M3 - Article
AN - SCOPUS:85071611116
VL - 481
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
M1 - 123455
ER -