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Lie's reduction method and differential Galois theory in the complex analytic context
Mixed initial-boundary value problem for Ott-Sudan-Ostrovskiy equation
1. | Instituto de Física y Matemáticas, UMSNH, Edificio C-3, Ciudad Universitaria), Morelia CP 58040, Michoacán, Mexico |
2. | Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico |
References:
[1] |
Hans-Dieter Alber and Peicheng Zhu, Global solutions to an initial boundary value problem for the Mullins equation,, J. Partial Differential Equations, 20 (2007), 30.
|
[2] |
Ravi P. Agarwal, Donal O'Regan and Svatoslav Staněk, Positive and maximal positive solutions of singular mixed boundary value problem,, Cent. Eur. J. Math., 7 (2009), 694.
doi: 10.2478/s11533-009-0049-9. |
[3] |
T. Buchukuri, O. Chkadua and D. Natroshvili, Mixed boundary value problems of thermopiezoelectricity for solids with interior cracks,, Integral Equations Operator Theory, 64 (2009), 495.
doi: 10.1007/s00020-009-1694-x. |
[4] |
Mouffak Benchohra and Samira Hamani, Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative,, Topol. Methods Nonlinear Anal., 32 (2008), 115.
|
[5] |
R. Brown, I. Mitrea, M. Mitrea and M. Wright, Mixed boundary value problems for the Stokes system,, Trans. Amer. Math. Soc., 362 (2010), 1211.
doi: 10.1090/S0002-9947-09-04774-6. |
[6] |
Jean-François Coulombel, Stability of finite difference schemes for hyperbolic initial boundary value problems,, SIAM J. Numer. Anal., 47 (2009), 2844.
doi: 10.1137/080728342. |
[7] |
Gilles Carbou and Bernard Hanouzet, Relaxation approximation of the Kerr model for the three-dimensional initial-boundary value problem,, J. Hyperbolic Differ. Equ., 6 (2009), 577.
doi: 10.1142/S0219891609001939. |
[8] |
I. Chudinovich and C. Constanda, The traction initial-boundary value problem for bending of thermoelastic plates with cracks,, Appl. Anal., 88 (2009), 961.
doi: 10.1080/00036810903042224. |
[9] |
F. D. Gakhov, Boundary value problems,, Pergamon Press, (1966).
|
[10] |
A. S. Fokas, The Davey-Stewartson equation on the half-plane,, Comm. Math. Phys., 289 (2009), 957.
doi: 10.1007/s00220-009-0809-1. |
[11] |
Yiping Fu and Yongsheng Li, Initial boundary value problem for generalized 2D complex Ginzburg-Landau equation,, J. Partial Differential Equations, 20 (2007), 65.
|
[12] |
Helmut Friedrich, Initial boundary value problems for Einstein's field equations and geometric uniqueness,, Gen. Relativity Gravitation, 41 (2009), 1947.
doi: 10.1007/s10714-009-0800-3. |
[13] |
N. Hayashi, E. I. Kaikina, P. I. Naumkin and I. A. Shishmarev, "Asymptotics for Dissipative Nonlinear Equations,", Lecture Notes in Mathematics, 1884 (2006).
|
[14] |
Nakao Hayashi and Elena Kaikina, "Nonlinear Theory of Pseudodifferential Equations on a Half-line,", North-Holland Mathematics Studies, 194 (2004).
|
[15] |
Elena I. Kaikina, Subcritical pseudodifferential equation on a half-line with nonanalytic symbol,, Differential Integral Equations, 18 (2005), 1341.
|
[16] |
Elena I. Kaikina, Pseudodifferential operator with a nonanalytic symbol on a half-line,, J. of Mathematical Physics, 48 (2007).
doi: 10.1063/1.2804860. |
[17] |
Elena I. Kaikina, Critical Ostrovskiy-type equation on a half-line,, Differential Integral Equations, 22 (2009), 69.
|
[18] |
Elena I. Kaikina, Ott-Sudan-Ostrovskiy type equations on a segment with large initial data,, Z. Angew. Math. Phys., 59 (2008), 647.
doi: 10.1007/s00033-007-6075-1. |
[19] |
Elena I. Kaikina, Nonlinear pseudoparabolic type equations on a half-line with large initial data,, Nonlinear Anal., 67 (2007), 2839.
doi: 10.1016/j.na.2006.09.044. |
[20] |
L. A. Ostrovsky, Short-wave asymptotics for weak shock waves and solitons in mechanics,, Int. J. Non-Linear Mechanics, 11 (1976), 401.
doi: 10.1016/0020-7462(76)90026-3. |
[21] |
E. Ott and R. N. Sudan, Nonlinear theory of ion acoustic waves with Landau damping,, Phys. Fluids, 12 (1969), 2388.
doi: 10.1063/1.1692358. |
[22] |
S. G. Samko, A. A. Kilbas and O. I. Marichev, "Fractional Integrals and Derivatives. Theory and Applications,", Gordon and Breach Science Publishers, (1993).
|
[23] |
Zhi-Qiang Shao, Global existence of classical solutions to the mixed initial-boundary value problem for quasilinear hyperbolic systems of diagonal form with large BV data,, J. Math. Anal. Appl., 360 (2009), 398.
doi: 10.1016/j.jmaa.2009.06.066. |
[24] |
Sheng Zhang, A domain embedding method for mixed boundary value problems,, C. R. Math. Acad. Sci. Paris, 343 (2006), 287.
|
show all references
References:
[1] |
Hans-Dieter Alber and Peicheng Zhu, Global solutions to an initial boundary value problem for the Mullins equation,, J. Partial Differential Equations, 20 (2007), 30.
|
[2] |
Ravi P. Agarwal, Donal O'Regan and Svatoslav Staněk, Positive and maximal positive solutions of singular mixed boundary value problem,, Cent. Eur. J. Math., 7 (2009), 694.
doi: 10.2478/s11533-009-0049-9. |
[3] |
T. Buchukuri, O. Chkadua and D. Natroshvili, Mixed boundary value problems of thermopiezoelectricity for solids with interior cracks,, Integral Equations Operator Theory, 64 (2009), 495.
doi: 10.1007/s00020-009-1694-x. |
[4] |
Mouffak Benchohra and Samira Hamani, Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative,, Topol. Methods Nonlinear Anal., 32 (2008), 115.
|
[5] |
R. Brown, I. Mitrea, M. Mitrea and M. Wright, Mixed boundary value problems for the Stokes system,, Trans. Amer. Math. Soc., 362 (2010), 1211.
doi: 10.1090/S0002-9947-09-04774-6. |
[6] |
Jean-François Coulombel, Stability of finite difference schemes for hyperbolic initial boundary value problems,, SIAM J. Numer. Anal., 47 (2009), 2844.
doi: 10.1137/080728342. |
[7] |
Gilles Carbou and Bernard Hanouzet, Relaxation approximation of the Kerr model for the three-dimensional initial-boundary value problem,, J. Hyperbolic Differ. Equ., 6 (2009), 577.
doi: 10.1142/S0219891609001939. |
[8] |
I. Chudinovich and C. Constanda, The traction initial-boundary value problem for bending of thermoelastic plates with cracks,, Appl. Anal., 88 (2009), 961.
doi: 10.1080/00036810903042224. |
[9] |
F. D. Gakhov, Boundary value problems,, Pergamon Press, (1966).
|
[10] |
A. S. Fokas, The Davey-Stewartson equation on the half-plane,, Comm. Math. Phys., 289 (2009), 957.
doi: 10.1007/s00220-009-0809-1. |
[11] |
Yiping Fu and Yongsheng Li, Initial boundary value problem for generalized 2D complex Ginzburg-Landau equation,, J. Partial Differential Equations, 20 (2007), 65.
|
[12] |
Helmut Friedrich, Initial boundary value problems for Einstein's field equations and geometric uniqueness,, Gen. Relativity Gravitation, 41 (2009), 1947.
doi: 10.1007/s10714-009-0800-3. |
[13] |
N. Hayashi, E. I. Kaikina, P. I. Naumkin and I. A. Shishmarev, "Asymptotics for Dissipative Nonlinear Equations,", Lecture Notes in Mathematics, 1884 (2006).
|
[14] |
Nakao Hayashi and Elena Kaikina, "Nonlinear Theory of Pseudodifferential Equations on a Half-line,", North-Holland Mathematics Studies, 194 (2004).
|
[15] |
Elena I. Kaikina, Subcritical pseudodifferential equation on a half-line with nonanalytic symbol,, Differential Integral Equations, 18 (2005), 1341.
|
[16] |
Elena I. Kaikina, Pseudodifferential operator with a nonanalytic symbol on a half-line,, J. of Mathematical Physics, 48 (2007).
doi: 10.1063/1.2804860. |
[17] |
Elena I. Kaikina, Critical Ostrovskiy-type equation on a half-line,, Differential Integral Equations, 22 (2009), 69.
|
[18] |
Elena I. Kaikina, Ott-Sudan-Ostrovskiy type equations on a segment with large initial data,, Z. Angew. Math. Phys., 59 (2008), 647.
doi: 10.1007/s00033-007-6075-1. |
[19] |
Elena I. Kaikina, Nonlinear pseudoparabolic type equations on a half-line with large initial data,, Nonlinear Anal., 67 (2007), 2839.
doi: 10.1016/j.na.2006.09.044. |
[20] |
L. A. Ostrovsky, Short-wave asymptotics for weak shock waves and solitons in mechanics,, Int. J. Non-Linear Mechanics, 11 (1976), 401.
doi: 10.1016/0020-7462(76)90026-3. |
[21] |
E. Ott and R. N. Sudan, Nonlinear theory of ion acoustic waves with Landau damping,, Phys. Fluids, 12 (1969), 2388.
doi: 10.1063/1.1692358. |
[22] |
S. G. Samko, A. A. Kilbas and O. I. Marichev, "Fractional Integrals and Derivatives. Theory and Applications,", Gordon and Breach Science Publishers, (1993).
|
[23] |
Zhi-Qiang Shao, Global existence of classical solutions to the mixed initial-boundary value problem for quasilinear hyperbolic systems of diagonal form with large BV data,, J. Math. Anal. Appl., 360 (2009), 398.
doi: 10.1016/j.jmaa.2009.06.066. |
[24] |
Sheng Zhang, A domain embedding method for mixed boundary value problems,, C. R. Math. Acad. Sci. Paris, 343 (2006), 287.
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