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Large-time asymptotics of the generalized Benjamin-Ono-Burgers equation
A doubly nonlinear parabolic equation with a singular potential
1. | Université de La Rochelle, Laboratoire MIA, Avenue Michel Crépeau, F-17042 La Rochelle Cedex, France |
2. | Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, I-41100 Modena, Italy |
3. | Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France |
References:
[1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations,", North-Holland, (1992).
|
[2] |
L. Cherfils, S. Gatti and A. Miranville, Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potential,, J. Math. Anal. Appl., 343 (2008), 557.
doi: doi:10.1016/j.jmaa.2008.01.077. |
[3] |
L. Cherfils, S. Gatti and A. Miranville, Corrigendum to "Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potential,", J. Math. Anal. Appl., 348 (2008), 1029.
doi: doi:10.1016/j.jmaa.2008.07.058. |
[4] |
A. Eden, C. Foias, B. Nicolaenko and R.Temam, "Exponential Attractors for Dissipative Evolution Equations,", in, 37 (1994).
|
[5] |
A. Eden, B. Michaux and J.-M. Rakotoson, Doubly nonlinear parabolic-type equations as dynamical systems,, J. Dyn. Diff. Eqns., 3 (1991), 87.
doi: doi:10.1007/BF01049490. |
[6] |
A. Eden and J.-M. Rakotoson, Exponential attractors for a doubly nonlinear equation,, J. Math. Anal. Appl., 185 (1994), 321.
doi: doi:10.1006/jmaa.1994.1251. |
[7] |
M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance,, Physica D, 92 (1996), 178.
doi: doi:10.1016/0167-2789(95)00173-5. |
[8] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,", in, 23 (1967).
|
[9] |
J. Málek and D. Prážak, Large time behavior via the method of $l$-trajectories,, J. Diff. Eqns., 181 (2002), 243.
doi: doi:10.1006/jdeq.2001.4087. |
[10] |
A. Miranville, Finite dimensional global attractor for a class of doubly nonlinear parabolic equations,, Cent. Eur. J. Math., 4 (2006), 163.
doi: doi:10.1007/s11533-005-0010-5. |
[11] |
A. Miranville and S. Zelik, Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type,, Nonlinearity, 20 (2007), 1773.
doi: doi:10.1088/0951-7715/20/8/001. |
[12] |
A. Rougirel, Convergence to steady state and attractors for doubly nonlinear equations,, J. Math. Anal. Appl., 339 (2008), 281.
doi: doi:10.1016/j.jmaa.2007.06.028. |
[13] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics,", Springer, (1988).
|
show all references
References:
[1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations,", North-Holland, (1992).
|
[2] |
L. Cherfils, S. Gatti and A. Miranville, Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potential,, J. Math. Anal. Appl., 343 (2008), 557.
doi: doi:10.1016/j.jmaa.2008.01.077. |
[3] |
L. Cherfils, S. Gatti and A. Miranville, Corrigendum to "Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potential,", J. Math. Anal. Appl., 348 (2008), 1029.
doi: doi:10.1016/j.jmaa.2008.07.058. |
[4] |
A. Eden, C. Foias, B. Nicolaenko and R.Temam, "Exponential Attractors for Dissipative Evolution Equations,", in, 37 (1994).
|
[5] |
A. Eden, B. Michaux and J.-M. Rakotoson, Doubly nonlinear parabolic-type equations as dynamical systems,, J. Dyn. Diff. Eqns., 3 (1991), 87.
doi: doi:10.1007/BF01049490. |
[6] |
A. Eden and J.-M. Rakotoson, Exponential attractors for a doubly nonlinear equation,, J. Math. Anal. Appl., 185 (1994), 321.
doi: doi:10.1006/jmaa.1994.1251. |
[7] |
M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance,, Physica D, 92 (1996), 178.
doi: doi:10.1016/0167-2789(95)00173-5. |
[8] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,", in, 23 (1967).
|
[9] |
J. Málek and D. Prážak, Large time behavior via the method of $l$-trajectories,, J. Diff. Eqns., 181 (2002), 243.
doi: doi:10.1006/jdeq.2001.4087. |
[10] |
A. Miranville, Finite dimensional global attractor for a class of doubly nonlinear parabolic equations,, Cent. Eur. J. Math., 4 (2006), 163.
doi: doi:10.1007/s11533-005-0010-5. |
[11] |
A. Miranville and S. Zelik, Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type,, Nonlinearity, 20 (2007), 1773.
doi: doi:10.1088/0951-7715/20/8/001. |
[12] |
A. Rougirel, Convergence to steady state and attractors for doubly nonlinear equations,, J. Math. Anal. Appl., 339 (2008), 281.
doi: doi:10.1016/j.jmaa.2007.06.028. |
[13] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics,", Springer, (1988).
|
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