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The global solvability of a sixth order Cahn-Hilliard type equation via the Bäcklund transformation
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A BKM's criterion of smooth solution to the incompressible viscoelastic flow
Convergence rate to strong boundary layer solutions for generalized BBM-Burgers equations with non-convex 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 Benjamin-Bona-Mahony equation, Indian J. Pure Appl. Math., 43 (2012), 323-342.
doi: 10.1007/s13226-012-0020-5. |
[2] |
E. Grenier and F. Rousset, Stability of one-dimensional boundary layers by using Green's functions, Communications on Pure and Applied Mathematics, 54 (2001), 1343-1385.
doi: DOI: 10.1002/cpa.10006. |
[3] |
Y. Kagei and S. Kawashima, Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space, Commun. Math. Phys., 266 (2006), 401-430.
doi: 10.1007/s00220-006-0017-1. |
[4] |
S. Kawashima and A. Matsumura, Asymptotic stability of travelling wave solutions of systems for one-dimensional gas motion, Commun. Math. Phys., 101 (1985), 97-127.
doi: 10.1007/BF01212358. |
[5] |
S. Kawashima and A. Matsumura, Stability of shock profiles in viscoelasticity with non-convex constitutive relations, Commun. Pure Appl. Math., 47 (1994), 1547-1569.
doi: 10.1002/cpa.3160471202. |
[6] |
S. Kawashima, S. Nishibata and M. Nishikawa, Asymptotic stability of stationary waves for two-dimensional viscous conservation laws in half plane, Discrete and Continuous Dynamical Systems, Supplement (2003), 469-476. |
[7] |
S. Kawashima, S. Nishibata and M. Nishikawa, $L^p$ energy method for multi-dimensional viscous coonservation laws and applications to the stability of planar waves, J. Hyperbolic Differential Equations, 1 (2004), 581-603.
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), 296-320.
doi: 10.1006/jdeq.1996.3217. |
[9] |
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex nonlinearity, Commun. Math. Phys., 165 (1994), 83-96.
doi: 10.1007/BF02099739. |
[10] |
T. Nakamura, S. Nishibata and, T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line, J. Differential Equations, 241 (2007), 94-111.
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), 107-132. |
[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), 329-343. |
[13] |
H. Yin and H. J. Zhao, Nonlinear stability of boundary layer solutions for generalized Benjamin-Bona-Mahony-Burgers equations in the half-space, Kinetic and Related Models, 2 (2009), 3144-3216. |
[14] |
H. Yin, H. J. Zhao and J. S. Kim, Convergence rates of solutions toward boundary layer solutions for generalized Benjamin-Bona-Mahony-Burgers equations in the half-space, J. Differential Equations, 245 (2008), 3144-3216.
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), 273-306.
doi: 10.1006/jdeq.2001.4063. |
[16] |
P. C. Zhu, Nonlinear Waves for the Compressible Navier-Stokes Equations in the Half Space, the report for JSPS postdoctoral research at Kyushu University, Fukuoka, Japan, August 2001. |
show all references
References:
[1] |
H. P. Cui, The asymptotic behavior of solutions of an initial boundary value problem for the generalized Benjamin-Bona-Mahony equation, Indian J. Pure Appl. Math., 43 (2012), 323-342.
doi: 10.1007/s13226-012-0020-5. |
[2] |
E. Grenier and F. Rousset, Stability of one-dimensional boundary layers by using Green's functions, Communications on Pure and Applied Mathematics, 54 (2001), 1343-1385.
doi: DOI: 10.1002/cpa.10006. |
[3] |
Y. Kagei and S. Kawashima, Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space, Commun. Math. Phys., 266 (2006), 401-430.
doi: 10.1007/s00220-006-0017-1. |
[4] |
S. Kawashima and A. Matsumura, Asymptotic stability of travelling wave solutions of systems for one-dimensional gas motion, Commun. Math. Phys., 101 (1985), 97-127.
doi: 10.1007/BF01212358. |
[5] |
S. Kawashima and A. Matsumura, Stability of shock profiles in viscoelasticity with non-convex constitutive relations, Commun. Pure Appl. Math., 47 (1994), 1547-1569.
doi: 10.1002/cpa.3160471202. |
[6] |
S. Kawashima, S. Nishibata and M. Nishikawa, Asymptotic stability of stationary waves for two-dimensional viscous conservation laws in half plane, Discrete and Continuous Dynamical Systems, Supplement (2003), 469-476. |
[7] |
S. Kawashima, S. Nishibata and M. Nishikawa, $L^p$ energy method for multi-dimensional viscous coonservation laws and applications to the stability of planar waves, J. Hyperbolic Differential Equations, 1 (2004), 581-603.
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), 296-320.
doi: 10.1006/jdeq.1996.3217. |
[9] |
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex nonlinearity, Commun. Math. Phys., 165 (1994), 83-96.
doi: 10.1007/BF02099739. |
[10] |
T. Nakamura, S. Nishibata and, T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line, J. Differential Equations, 241 (2007), 94-111.
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), 107-132. |
[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), 329-343. |
[13] |
H. Yin and H. J. Zhao, Nonlinear stability of boundary layer solutions for generalized Benjamin-Bona-Mahony-Burgers equations in the half-space, Kinetic and Related Models, 2 (2009), 3144-3216. |
[14] |
H. Yin, H. J. Zhao and J. S. Kim, Convergence rates of solutions toward boundary layer solutions for generalized Benjamin-Bona-Mahony-Burgers equations in the half-space, J. Differential Equations, 245 (2008), 3144-3216.
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), 273-306.
doi: 10.1006/jdeq.2001.4063. |
[16] |
P. C. Zhu, Nonlinear Waves for the Compressible Navier-Stokes Equations in the Half Space, the report for JSPS postdoctoral research at Kyushu University, Fukuoka, Japan, August 2001. |
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