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
N1 - Funding Information:
The authors would like to thank the anonymous referees for their helpful comments. The first author (Y. Z. Wang) is partially supported by the National Natural Science Foundation of China ( 11871212 ) and Innovation Scientists and Plan for Scientific Innovation Talent of Henan Province (Grant No. 154100510012 ). The second author (J. Xu) is partially supported by the National Natural Science Foundation of China ( 11471158 ) and the Fundamental Research Funds for the Central Universities ( NE2015005 ). The third author (S. Kawashima) is partially supported by Grant-in-Aid for Scientific Researches (S) 25220702 .
Publisher Copyright:
© 2019 Elsevier Inc.
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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U2 - 10.1016/j.jmaa.2019.123455
DO - 10.1016/j.jmaa.2019.123455
M3 - Article
AN - SCOPUS:85071611116
SN - 0022-247X
VL - 481
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 123455
ER -