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Global stability of stationary waves for damped wave equations
1. | Department of Mathematics and Physics, Wuhan Polytechnic University, Wuhan 430023, China |
2. | Department of Mathematics, Jinan University, Guangzhou 510632, China |
3. | School of Mathematics and Statistics, Wuhan University, Wuhan 430072 |
4. | College of Science, Wuhan University of Science and Technology, Wuhan 430081, China |
References:
[1] |
R. A. Adams, Sobolev Spaces,, Pure and Applied Mathematics, (1975).
|
[2] |
L.-L. Fan, H.-X. Liu and H. Yin, Decay estimates of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space,[Decay estimates of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space], Acta Mathematica Scientia Ser. B Engl. Ed., 31 (2011), 1389.
doi: 10.1016/S0252-9602(11)60326-3. |
[3] |
L.-L. Fan, H.-X. Liu and H.-J. Zhao, One-dimensional damped wave equation with large initial perturbation,, Analysis and Applications, 11 (2013).
doi: 10.1142/S0219530513500139. |
[4] |
L.-L. Fan, H.-X. Liu and H.-J. Zhao, Nonlinear stability of planar boundary layer solutions for damped wave equation,, J. Hyperbolic Differ. Equ., 8 (2011), 545.
doi: 10.1142/S0219891611002494. |
[5] |
L.-L. Fan, H. Yin and H.-J. Zhao, Decay rates toward stationary waves of solutions for damped wave equations,, J. Partial Differential Equations, 21 (2008), 141.
|
[6] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion,, Comm. Math. Phys., 101 (1985), 97.
doi: 10.1007/BF01212358. |
[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.
doi: 10.1142/S0219891604000196. |
[8] |
T.-P. Liu, A. Matsumura and K. Nishihara, Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves,, SIAM J. Math. Anal., 29 (1998), 293.
doi: 10.1137/S0036141096306005. |
[9] |
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. |
[10] |
R. Natalini, Convergence to equilibrium for the relaxation approximations of conservation laws,, Comm. Pure Appl. Math., 49 (1996), 795.
doi: 10.1002/(SICI)1097-0312(199608)49:8<795::AID-CPA2>3.0.CO;2-3. |
[11] |
Y. Ueda, Asymptotic stability of stationary waves for damped wave equations with a nonlinear convection term,, Adv. Math. Sci. Appl., 18 (2008), 329.
|
[12] |
Y. Ueda and S. Kawashima, Large time behavior of solutions to a semilinear hyperbolic system with relaxation,, J. Hyperbolic Differ. Equ., 4 (2007), 147. Google Scholar |
[13] |
Y. Ueda, T. Nakamura and S. Kawashima, Stability of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space,, Kinetic and Related Models, 1 (2008), 49.
doi: 10.3934/krm.2008.1.49. |
[14] |
Y. Ueda, T. Nakamura and S. Kawashima, Stability of degenerate stationary waves for viscous gases,, Arch. Ration. Mech. Anal., 198 (2010), 735.
doi: 10.1007/s00205-010-0369-8. |
[15] |
Y. Ueda, T. Nakamura and S. Kawashima, Energy method in the partial Fourier space and application to stability problems in the half space,, J. Differential Equations, 250 (2011), 1169.
doi: 10.1016/j.jde.2010.10.003. |
show all references
References:
[1] |
R. A. Adams, Sobolev Spaces,, Pure and Applied Mathematics, (1975).
|
[2] |
L.-L. Fan, H.-X. Liu and H. Yin, Decay estimates of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space,[Decay estimates of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space], Acta Mathematica Scientia Ser. B Engl. Ed., 31 (2011), 1389.
doi: 10.1016/S0252-9602(11)60326-3. |
[3] |
L.-L. Fan, H.-X. Liu and H.-J. Zhao, One-dimensional damped wave equation with large initial perturbation,, Analysis and Applications, 11 (2013).
doi: 10.1142/S0219530513500139. |
[4] |
L.-L. Fan, H.-X. Liu and H.-J. Zhao, Nonlinear stability of planar boundary layer solutions for damped wave equation,, J. Hyperbolic Differ. Equ., 8 (2011), 545.
doi: 10.1142/S0219891611002494. |
[5] |
L.-L. Fan, H. Yin and H.-J. Zhao, Decay rates toward stationary waves of solutions for damped wave equations,, J. Partial Differential Equations, 21 (2008), 141.
|
[6] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion,, Comm. Math. Phys., 101 (1985), 97.
doi: 10.1007/BF01212358. |
[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.
doi: 10.1142/S0219891604000196. |
[8] |
T.-P. Liu, A. Matsumura and K. Nishihara, Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves,, SIAM J. Math. Anal., 29 (1998), 293.
doi: 10.1137/S0036141096306005. |
[9] |
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. |
[10] |
R. Natalini, Convergence to equilibrium for the relaxation approximations of conservation laws,, Comm. Pure Appl. Math., 49 (1996), 795.
doi: 10.1002/(SICI)1097-0312(199608)49:8<795::AID-CPA2>3.0.CO;2-3. |
[11] |
Y. Ueda, Asymptotic stability of stationary waves for damped wave equations with a nonlinear convection term,, Adv. Math. Sci. Appl., 18 (2008), 329.
|
[12] |
Y. Ueda and S. Kawashima, Large time behavior of solutions to a semilinear hyperbolic system with relaxation,, J. Hyperbolic Differ. Equ., 4 (2007), 147. Google Scholar |
[13] |
Y. Ueda, T. Nakamura and S. Kawashima, Stability of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space,, Kinetic and Related Models, 1 (2008), 49.
doi: 10.3934/krm.2008.1.49. |
[14] |
Y. Ueda, T. Nakamura and S. Kawashima, Stability of degenerate stationary waves for viscous gases,, Arch. Ration. Mech. Anal., 198 (2010), 735.
doi: 10.1007/s00205-010-0369-8. |
[15] |
Y. Ueda, T. Nakamura and S. Kawashima, Energy method in the partial Fourier space and application to stability problems in the half space,, J. Differential Equations, 250 (2011), 1169.
doi: 10.1016/j.jde.2010.10.003. |
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