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Global conservative solutions to the Camassa--Holm equation for initial data with nonvanishing asymptotics
1. | Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway, Norway |
2. | Centre of Mathematics for Applications, University of Oslo, NO-0316 Oslo, Norway |
References:
[1] |
M. Bendahmane, G. M. Coclite and K. H. Karlsen, $H^1$-perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation, Mediterranean Journal of Mathematics, 3 (2006), 419-432. |
[2] |
A. Bressan and A. Constantin, Global conservative solutions of the Camassa-Holm equation, Arch. Ration. Mech. Anal., 183 (2007), 215-239. |
[3] |
A. Bressan and A. Constantin, Global dissipative solutions of the Camassa-Holm equation, Analysis and Applications, 5 (2007), 1-27. |
[4] |
A. Bressan, H. Holden and X. Raynaud, Lipschitz metric for the Hunter-Saxton equation, J. Math. Pures Appl., 94 (2010), 68-92. |
[5] |
R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solutions, Phys. Rev. Lett., 71 (1993), 1661-1664.
doi: 10.1103/PhysRevLett.71.1661. |
[6] |
R. Camassa, D. D. Holm and J. Hyman, A new integrable shallow water equation, Adv. Appl. Mech., 31 (1994), 1-33.
doi: 10.1016/S0065-2156(08)70254-0. |
[7] |
A. Constantin, Finite propagation speed for the Camassa-Holm equation, J. Math. Phys., 41 (2005), 023506. |
[8] |
A. Constantin and J. Escher, Wave breaking for nonlinear nonlocal shallow water equations, Acta Math., 181 (1998), 229-243.
doi: 10.1007/BF02392586. |
[9] |
A. Constantin and D. Lannes, The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations, Arch. Rat. Mech. Anal., 192 (2009), 165-186.
doi: 10.1007/s00205-008-0128-2. |
[10] |
K. Grunert, H. Holden and X. Raynaud, Lipschitz metric for the periodic Camassa-Holm equation, J. Differential Equations, 250 (2011), 1460-1492.
doi: 10.1016/j.jde.2010.07.006. |
[11] |
K. Grunert, H. Holden and X. Raynaud, Lipschitz metric for the Camassa-Holm equation on the line,, Discrete Contin. Dyn. Syst., ().
|
[12] |
H. Holden and X. Raynaud, Global conservative solutions for the Camassa-Holm equation - a Lagrangian point of view, Comm. Partial Differential Equations, 32 (2007), 1511-1549.
doi: 10.1080/03605300601088674. |
[13] |
H. Holden and X. Raynaud, Global conservative solutions of the generalized hyperelastic-rod wave equation, J. Differential Equations, 233 (2007), 448-484.
doi: 10.1016/j.jde.2006.09.007. |
[14] |
H. Holden and X. Raynaud, Dissipative solutions of the Camassa-Holm equation, Discrete Contin. Dyn. Syst., 24 (2009), 1047-1112.
doi: 10.3934/dcds.2009.24.1047. |
[15] |
H. Holden and X. Raynaud, Periodic conservative solutions of the Camassa-Holm equation, Ann. Inst. Fourier (Grenoble), 58 (2008), 945-988.
doi: 10.5802/aif.2375. |
[16] |
J. Lenells, Traveling wave solutions of the Camassa-Holm equation, J. Differential Equations, 217 (2005), 393-430.
doi: 10.1016/j.jde.2004.09.007. |
[17] |
J. Lenells, Classification of all traveling-wave solutions for some nonlinear dispersive equations, Phil. Trans. R. Soc. A, 365 (2007), 2291-2298.
doi: 10.1098/rsta.2007.2009. |
show all references
References:
[1] |
M. Bendahmane, G. M. Coclite and K. H. Karlsen, $H^1$-perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation, Mediterranean Journal of Mathematics, 3 (2006), 419-432. |
[2] |
A. Bressan and A. Constantin, Global conservative solutions of the Camassa-Holm equation, Arch. Ration. Mech. Anal., 183 (2007), 215-239. |
[3] |
A. Bressan and A. Constantin, Global dissipative solutions of the Camassa-Holm equation, Analysis and Applications, 5 (2007), 1-27. |
[4] |
A. Bressan, H. Holden and X. Raynaud, Lipschitz metric for the Hunter-Saxton equation, J. Math. Pures Appl., 94 (2010), 68-92. |
[5] |
R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solutions, Phys. Rev. Lett., 71 (1993), 1661-1664.
doi: 10.1103/PhysRevLett.71.1661. |
[6] |
R. Camassa, D. D. Holm and J. Hyman, A new integrable shallow water equation, Adv. Appl. Mech., 31 (1994), 1-33.
doi: 10.1016/S0065-2156(08)70254-0. |
[7] |
A. Constantin, Finite propagation speed for the Camassa-Holm equation, J. Math. Phys., 41 (2005), 023506. |
[8] |
A. Constantin and J. Escher, Wave breaking for nonlinear nonlocal shallow water equations, Acta Math., 181 (1998), 229-243.
doi: 10.1007/BF02392586. |
[9] |
A. Constantin and D. Lannes, The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations, Arch. Rat. Mech. Anal., 192 (2009), 165-186.
doi: 10.1007/s00205-008-0128-2. |
[10] |
K. Grunert, H. Holden and X. Raynaud, Lipschitz metric for the periodic Camassa-Holm equation, J. Differential Equations, 250 (2011), 1460-1492.
doi: 10.1016/j.jde.2010.07.006. |
[11] |
K. Grunert, H. Holden and X. Raynaud, Lipschitz metric for the Camassa-Holm equation on the line,, Discrete Contin. Dyn. Syst., ().
|
[12] |
H. Holden and X. Raynaud, Global conservative solutions for the Camassa-Holm equation - a Lagrangian point of view, Comm. Partial Differential Equations, 32 (2007), 1511-1549.
doi: 10.1080/03605300601088674. |
[13] |
H. Holden and X. Raynaud, Global conservative solutions of the generalized hyperelastic-rod wave equation, J. Differential Equations, 233 (2007), 448-484.
doi: 10.1016/j.jde.2006.09.007. |
[14] |
H. Holden and X. Raynaud, Dissipative solutions of the Camassa-Holm equation, Discrete Contin. Dyn. Syst., 24 (2009), 1047-1112.
doi: 10.3934/dcds.2009.24.1047. |
[15] |
H. Holden and X. Raynaud, Periodic conservative solutions of the Camassa-Holm equation, Ann. Inst. Fourier (Grenoble), 58 (2008), 945-988.
doi: 10.5802/aif.2375. |
[16] |
J. Lenells, Traveling wave solutions of the Camassa-Holm equation, J. Differential Equations, 217 (2005), 393-430.
doi: 10.1016/j.jde.2004.09.007. |
[17] |
J. Lenells, Classification of all traveling-wave solutions for some nonlinear dispersive equations, Phil. Trans. R. Soc. A, 365 (2007), 2291-2298.
doi: 10.1098/rsta.2007.2009. |
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