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Evolution Equations and Control Theory (EECT)
 

Asymptotic profile of solutions to the linearized double dispersion equation on the half space $\mathbb{R}^{n}_+$
Pages: 629 - 645, Issue 4, December 2017

doi:10.3934/eect.2017032      Abstract        References        Full text (396.1K)           Related Articles

Yu-Zhu Wang - School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China (email)
Si Chen - School of Sciences, Zhejiang Tongji Vocational College of Science and Technology, Hangzhou 310001, China (email)
Menglong Su - School of Mathematics, Luoyang Normal University, Luoyang 471934, China (email)

1 G. Chen, Y. Wang and S. Wang, Initial boundary value problem of the generalized cubic double dispersion equation, J. Math. Anal. Appl., 299 (2004), 563-577.       
2 G. Chen and H. Xue, Periodic boundary value problem and Cauchy problem of the generalized cubic double dispersion equation, Acta Math. Scientia, 28 (2008), 573-587.       
3 D. Hoff and K. Zumbrum, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow, Indiana Univ. Math. J., 44 (1995), 603-676.
4 X. Hu and Y. Z. Wang, Asymptotic profiles of solutions to two dimensional degenerated wave equation with damping, submitted.
5 R. Ikehata, New decay estimates for linear damped wave equations and its application to nonlinear problem, Math. Meth. Appl. Sci., 27 (2004), 865-889.       
6 R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Differential Equations, 257 (2014), 2159-2177.       
7 R. Ikehata, Some remarks on the asymptotic profiles of solutions for strongly damped wave equations on the 1-D half space, J. Math. Anal. Appl., 421 (2015), 905-916.
8 M. Kato, Y.-Z. Wang and S. Kawashima, Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension, Kinet. Relat. Models, 6 (2013), 969-987.       
9 S. Kawashima and Y.-Z. Wang, Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation, Analysis and Applications, 13 (2015), 233-254.       
10 T. Liu and W. Wang, The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimensions, Commun. Math. Phys., 196 (1998), 145-173.       
11 M. Liu and W. Wang, Global existence and pointwise estimates of solutions for the multidimensional generalized Boussinesq equation, Comm. Pure Appl. Anal., 13 (2014), 1203-1222.       
12 N. Polat and A. ErtaƟ, Existence and blow-up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation, J. Math. Anal. Appl., 349 (2009), 10-20.       
13 A. M. Samsonov, Nonlinear strain waves in elastic waveguides, in: Nonlinear Waves in Solids, CISM Coyrses and Lecture, Springer, 341 (1994), 349-382.       
14 A. M. Samsonov and E. V. Sokurinskaya, Energy exchange between nonlinear waves in elastic waveguides and external media, in: Nonlinear Waves in Active Media, Springer, Berlin, Heidelberg, 1989, 99-104.       
15 W. Wang, Nonlinear evolution systems and Green's function, Acta Math. Sci. Ser. B Engl. Ed., 30 (2010), 2051-2063.       
16 S. Wang and G. Chen, Cauchy problem of the generalized double dispersion equation, Nonlinear Anal., 64 (2006), 159-173.       
17 S. Wang and F. Da, On the asymptotic behavior of solution for the generalized double dipersion equation, Appl. Anal., 92 (2013), 1179-1193.       
18 Y.-Z. Wang and S. Chen, Asymptotic profile of solutions to the double dispersion equation, Nonlinear Anal., 134 (2016), 236-254.       
19 Y.-Z. Wang and H. Zhao, Pointwise estimates of global small solutions to the generalized double dispersion equation, J. Math. Anal. Appl., 448 (2017), 672-690.       
20 Y.-Z. Wang, S. Kawashima and J. Xu, Optimal decay estimates of solutions to the generalized double dispersion equation, preprint.
21 Z. Wu and W. Wang, Refined pointwise estimates for the Navier-Stokes-Poisson equations, Anal. Appl., 14 (2016), 739-762.
22 R. Xu, Y. Liu and T. Yu, Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations, Nonlinear Anal., 71 (2009), 4977-4983.       
23 Z. Yang, Global attractor for a nonlinear wave equation arising in elastic waveguide model, Nonlinear Anal., 70 (2009), 2132-2142.       
24 Z. Yang, A global attractor for the elastic waveguide model in $\mathbbR^n$, Nonlinear Anal., 74 (2011), 6640-6661.       
25 Z. Yang and K. Li, Longtime dynamics for a elastic waveguide model, Discrete Contin. Dyn. Syst., (2013), 797-806.       
26 Z. Yang, N. Feng and T. Ma, Global attractor for the generalized double dispersion equation, Nonlinear Anal., 115 (2015), 103-116.

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