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

被引：5

作者：

Wang, Yuzhu ^{[1
]}

Xu, Jiang ^{[2
]}

Kawashima, Shuichi ^{[3
]}

机构：

[1] North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450011, Henan, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211106, Jiangsu, Peoples R China

[3] Waseda Univ, Fac Sci & Engn, Tokyo 1698555, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 481卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Generalized double dispersion equation; Global existence; Optimal decay estimates; Critical Besov spaces; BOUNDARY-VALUE-PROBLEM; ASYMPTOTIC-BEHAVIOR; CAUCHY-PROBLEM; PLATE EQUATION; WAVE-EQUATION; ATTRACTOR; PROPERTY; RATES;

D O I：

10.1016/j.jmaa.2019.123455

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：22

共 33 条

[1]

[Anonymous], 1983, MONOGRAPH MATH

[2]

Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7

[3]

Chen GW, 2008, ACTA MATH SCI, V28, P573

[4] Initial boundary value problem of the generalized cubic double dispersion equation [J].

Chen, GW ;

Wang, YP ;

Wang, SB .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 299 (02) :563-577

[5] Optimal decay rates and asymptotic profile for the plate equation with structural damping [J].

Horbach, Jaqueline Luiza ;

Ikehata, Ryo ;

Charao, Ruy Coimbra .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 440 (02) :529-560

[6] Decay property of regularity-loss type for dissipative Timoshenko system [J].

Ide, Kentaro ;

Haramoto, Kazuo ;

Kawashima, Shuichi .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2008, 18 (05) :647-667

[7] Asymptotic profiles for wave equations with strong damping [J].

Ikehata, Ryo .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (06) :2159-2177

[8] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION IN ONE SPACE DIMENSION [J].

Kato, Masakazu ;

Wang, Yu-Zhu ;

Kawashima, Shuichi .

[9] Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation [J].

Kawashima, Shuichi ;

Wang, Yu-Zhu .

ANALYSIS AND APPLICATIONS, 2015, 13 (03) :233-254

[10] GLOBAL EXISTENCE AND DECAY OF SOLUTIONS FOR A QUASI-LINEAR DISSIPATIVE PLATE EQUATION [J].

Liu, Yongqin ;

Kawashima, Shuichi .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2011, 8 (03) :591-614

← 1 2 3 4 →