
Previous Article
A BKM's criterion of smooth solution to the incompressible viscoelastic flow
 CPAA Home
 This Issue

Next Article
The global solvability of a sixth order CahnHilliard type equation via the Bäcklund transformation
Convergence rate to strong boundary layer solutions for generalized BBMBurgers equations with nonconvex flux
1.  Department of Mathematics, University of Iowa, Iowa City, IA 52242 
2.  School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China 
References:
[1] 
H. P. Cui, The asymptotic behavior of solutions of an initial boundary value problem for the generalized BenjaminBonaMahony equation,, Indian J. Pure Appl. Math., 43 (2012), 323. doi: 10.1007/s1322601200205. 
[2] 
E. Grenier and F. Rousset, Stability of onedimensional boundary layers by using Green's functions,, Communications on Pure and Applied Mathematics, 54 (2001), 1343. doi: DOI: 10.1002/cpa.10006. 
[3] 
Y. Kagei and S. Kawashima, Stability of planar stationary solutions to the compressible NavierStokes equation on the half space,, Commun. Math. Phys., 266 (2006), 401. doi: 10.1007/s0022000600171. 
[4] 
S. Kawashima and A. Matsumura, Asymptotic stability of travelling wave solutions of systems for onedimensional gas motion,, Commun. Math. Phys., 101 (1985), 97. doi: 10.1007/BF01212358. 
[5] 
S. Kawashima and A. Matsumura, Stability of shock profiles in viscoelasticity with nonconvex constitutive relations,, Commun. Pure Appl. Math., 47 (1994), 1547. doi: 10.1002/cpa.3160471202. 
[6] 
S. Kawashima, S. Nishibata and M. Nishikawa, Asymptotic stability of stationary waves for twodimensional viscous conservation laws in half plane,, Discrete and Continuous Dynamical Systems, Supplement (2003), 469. 
[7] 
S. Kawashima, S. Nishibata and M. Nishikawa, $L^p$ energy method for multidimensional viscous coonservation laws and applications to the stability of planar waves,, J. Hyperbolic Differential Equations, 1 (2004), 581. doi: 10.1142/S0219891604000196. 
[8] 
T. P. Liu and K. Nishihara, Asymptotic behavior for scalar viscous conservation laws with boundary effect,, J. Differential Equations, 133 (1997), 296. doi: 10.1006/jdeq.1996.3217. 
[9] 
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with nonconvex nonlinearity,, Commun. Math. Phys., 165 (1994), 83. doi: 10.1007/BF02099739. 
[10] 
T. Nakamura, S. Nishibata and, T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible NavierStokes equation in a half line,, J. Differential Equations, 241 (2007), 94. doi: 10.1016/j.jde.2007.06.016. 
[11] 
M. Nishikawa, Convergence rates to the travelling wave for viscous conservation laws,, Funk. Ekvac., 41 (1998), 107. 
[12] 
Y. Ueda, Asymptotic convergence toward stationary waves to the wave equation with a convection term in the half space,, Advances in Mathematical Sciences and Applications, 18 (2008), 329. 
[13] 
H. Yin and H. J. Zhao, Nonlinear stability of boundary layer solutions for generalized BenjaminBonaMahonyBurgers equations in the halfspace,, Kinetic and Related Models, 2 (2009), 3144. 
[14] 
H. Yin, H. J. Zhao and J. S. Kim, Convergence rates of solutions toward boundary layer solutions for generalized BenjaminBonaMahonyBurgers equations in the halfspace,, J. Differential Equations, 245 (2008), 3144. doi: 10.1016/j.jde.2007.12.012. 
[15] 
C. J. Zhu, Asymptotic behavior of solutions for $p$system with relaxation,, J. Differential Equations, 180 (2002), 273. doi: 10.1006/jdeq.2001.4063. 
[16] 
P. C. Zhu, Nonlinear Waves for the Compressible NavierStokes Equations in the Half Space,, the report for JSPS postdoctoral research at Kyushu University, (2001). 
show all references
References:
[1] 
H. P. Cui, The asymptotic behavior of solutions of an initial boundary value problem for the generalized BenjaminBonaMahony equation,, Indian J. Pure Appl. Math., 43 (2012), 323. doi: 10.1007/s1322601200205. 
[2] 
E. Grenier and F. Rousset, Stability of onedimensional boundary layers by using Green's functions,, Communications on Pure and Applied Mathematics, 54 (2001), 1343. doi: DOI: 10.1002/cpa.10006. 
[3] 
Y. Kagei and S. Kawashima, Stability of planar stationary solutions to the compressible NavierStokes equation on the half space,, Commun. Math. Phys., 266 (2006), 401. doi: 10.1007/s0022000600171. 
[4] 
S. Kawashima and A. Matsumura, Asymptotic stability of travelling wave solutions of systems for onedimensional gas motion,, Commun. Math. Phys., 101 (1985), 97. doi: 10.1007/BF01212358. 
[5] 
S. Kawashima and A. Matsumura, Stability of shock profiles in viscoelasticity with nonconvex constitutive relations,, Commun. Pure Appl. Math., 47 (1994), 1547. doi: 10.1002/cpa.3160471202. 
[6] 
S. Kawashima, S. Nishibata and M. Nishikawa, Asymptotic stability of stationary waves for twodimensional viscous conservation laws in half plane,, Discrete and Continuous Dynamical Systems, Supplement (2003), 469. 
[7] 
S. Kawashima, S. Nishibata and M. Nishikawa, $L^p$ energy method for multidimensional viscous coonservation laws and applications to the stability of planar waves,, J. Hyperbolic Differential Equations, 1 (2004), 581. doi: 10.1142/S0219891604000196. 
[8] 
T. P. Liu and K. Nishihara, Asymptotic behavior for scalar viscous conservation laws with boundary effect,, J. Differential Equations, 133 (1997), 296. doi: 10.1006/jdeq.1996.3217. 
[9] 
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with nonconvex nonlinearity,, Commun. Math. Phys., 165 (1994), 83. doi: 10.1007/BF02099739. 
[10] 
T. Nakamura, S. Nishibata and, T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible NavierStokes equation in a half line,, J. Differential Equations, 241 (2007), 94. doi: 10.1016/j.jde.2007.06.016. 
[11] 
M. Nishikawa, Convergence rates to the travelling wave for viscous conservation laws,, Funk. Ekvac., 41 (1998), 107. 
[12] 
Y. Ueda, Asymptotic convergence toward stationary waves to the wave equation with a convection term in the half space,, Advances in Mathematical Sciences and Applications, 18 (2008), 329. 
[13] 
H. Yin and H. J. Zhao, Nonlinear stability of boundary layer solutions for generalized BenjaminBonaMahonyBurgers equations in the halfspace,, Kinetic and Related Models, 2 (2009), 3144. 
[14] 
H. Yin, H. J. Zhao and J. S. Kim, Convergence rates of solutions toward boundary layer solutions for generalized BenjaminBonaMahonyBurgers equations in the halfspace,, J. Differential Equations, 245 (2008), 3144. doi: 10.1016/j.jde.2007.12.012. 
[15] 
C. J. Zhu, Asymptotic behavior of solutions for $p$system with relaxation,, J. Differential Equations, 180 (2002), 273. doi: 10.1006/jdeq.2001.4063. 
[16] 
P. C. Zhu, Nonlinear Waves for the Compressible NavierStokes Equations in the Half Space,, the report for JSPS postdoctoral research at Kyushu University, (2001). 
[1] 
Hui Yin, Huijiang Zhao. Nonlinear stability of boundary layer solutions for generalized BenjaminBonaMahonyBurgers equation in the half space. Kinetic & Related Models, 2009, 2 (3) : 521550. doi: 10.3934/krm.2009.2.521 
[2] 
Khaled El Dika. Asymptotic stability of solitary waves for the BenjaminBonaMahony equation. Discrete & Continuous Dynamical Systems  A, 2005, 13 (3) : 583622. doi: 10.3934/dcds.2005.13.583 
[3] 
Milena Stanislavova. On the global attractor for the damped BenjaminBonaMahony equation. Conference Publications, 2005, 2005 (Special) : 824832. doi: 10.3934/proc.2005.2005.824 
[4] 
Wenxia Chen, Ping Yang, Weiwei Gao, Lixin Tian. The approximate solution for BenjaminBonaMahony equation under slowly varying medium. Communications on Pure & Applied Analysis, 2018, 17 (3) : 823848. doi: 10.3934/cpaa.2018042 
[5] 
C. H. Arthur Cheng, John M. Hong, YingChieh Lin, Jiahong Wu, JuanMing Yuan. Wellposedness of the twodimensional generalized BenjaminBonaMahony equation on the upper half plane. Discrete & Continuous Dynamical Systems  B, 2016, 21 (3) : 763779. doi: 10.3934/dcdsb.2016.21.763 
[6] 
Vishal Vasan, Bernard Deconinck. Wellposedness of boundaryvalue problems for the linear BenjaminBonaMahony equation. Discrete & Continuous Dynamical Systems  A, 2013, 33 (7) : 31713188. doi: 10.3934/dcds.2013.33.3171 
[7] 
Jaime Angulo Pava, Carlos Banquet, Márcia Scialom. Stability for the modified and fourthorder BenjaminBonaMahony equations. Discrete & Continuous Dynamical Systems  A, 2011, 30 (3) : 851871. doi: 10.3934/dcds.2011.30.851 
[8] 
AnneSophie de Suzzoni. Continuity of the flow of the BenjaminBonaMahony equation on probability measures. Discrete & Continuous Dynamical Systems  A, 2015, 35 (7) : 29052920. doi: 10.3934/dcds.2015.35.2905 
[9] 
Yangrong Li, Renhai Wang, Jinyan Yin. Backward compact attractors for nonautonomous BenjaminBonaMahony equations on unbounded channels. Discrete & Continuous Dynamical Systems  B, 2017, 22 (7) : 25692586. doi: 10.3934/dcdsb.2017092 
[10] 
Jerry L. Bona, Laihan Luo. Largetime asymptotics of the generalized BenjaminOnoBurgers equation. Discrete & Continuous Dynamical Systems  S, 2011, 4 (1) : 1550. doi: 10.3934/dcdss.2011.4.15 
[11] 
Tong Li, Jeungeun Park. Stability of traveling waves of models for image processing with nonconvex nonlinearity. Communications on Pure & Applied Analysis, 2018, 17 (3) : 959985. doi: 10.3934/cpaa.2018047 
[12] 
Yongming Liu, Lei Yao. Global solution and decay rate for a reduced gravity two and a half layer model. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 26132638. doi: 10.3934/dcdsb.2018267 
[13] 
Peng Gao. Unique continuation property for stochastic nonclassical diffusion equations and stochastic linearized BenjaminBonaMahony equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 24932510. doi: 10.3934/dcdsb.2018262 
[14] 
. Adimurthi, Siddhartha Mishra, G.D. Veerappa Gowda. Existence and stability of entropy solutions for a conservation law with discontinuous nonconvex fluxes. Networks & Heterogeneous Media, 2007, 2 (1) : 127157. doi: 10.3934/nhm.2007.2.127 
[15] 
Yong Wang, Wanquan Liu, Guanglu Zhou. An efficient algorithm for nonconvex sparse optimization. Journal of Industrial & Management Optimization, 2017, 13 (5) : 113. doi: 10.3934/jimo.2018134 
[16] 
Dimitra Antonopoulou, Georgia Karali. Existence of solution for a generalized stochastic CahnHilliard equation on convex domains. Discrete & Continuous Dynamical Systems  B, 2011, 16 (1) : 3155. doi: 10.3934/dcdsb.2011.16.31 
[17] 
Zigen Ouyang, Chunhua Ou. Global stability and convergence rate of traveling waves for a nonlocal model in periodic media. Discrete & Continuous Dynamical Systems  B, 2012, 17 (3) : 9931007. doi: 10.3934/dcdsb.2012.17.993 
[18] 
Hirotada Honda. Globalintime solution and stability of KuramotoSakaguchi equation under nonlocal Coupling. Networks & Heterogeneous Media, 2017, 12 (1) : 2557. doi: 10.3934/nhm.2017002 
[19] 
Yoon Mo Jung, Taeuk Jeong, Sangwoon Yun. Nonconvex TV denoising corrupted by impulse noise. Inverse Problems & Imaging, 2017, 11 (4) : 689702. doi: 10.3934/ipi.2017032 
[20] 
Boling Guo, Zhaohui Huo. The global attractor of the damped, forced generalized Korteweg de VriesBenjaminOno equation in $L^2$. Discrete & Continuous Dynamical Systems  A, 2006, 16 (1) : 121136. doi: 10.3934/dcds.2006.16.121 
2017 Impact Factor: 0.884
Tools
Metrics
Other articles
by authors
[Back to Top]