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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, Amsterdam, 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), 557-566.
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), 1029-1030.
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 "Research in Applied Mathematics," Vol. 37, John-Wiley, New York, 1994. |
| [5] |
A. Eden, B. Michaux and J.-M. Rakotoson, Doubly nonlinear parabolic-type equations as dynamical systems, J. Dyn. Diff. Eqns., 3 (1991), 87-131.
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), 321-339.
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), 178-192.
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 "Translations of Mathematical Monographs," Vol. 23, American Mathematical Society, Providence, R.I., 1967. |
| [9] |
J. Málek and D. Prážak, Large time behavior via the method of $l$-trajectories, J. Diff. Eqns., 181 (2002), 243-279.
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), 163-182.
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), 1773-1797.
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), 281-294.
doi: doi:10.1016/j.jmaa.2007.06.028. |
| [13] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Springer, New York, 1988. |
show all references
References:
| [1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," North-Holland, Amsterdam, 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), 557-566.
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), 1029-1030.
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 "Research in Applied Mathematics," Vol. 37, John-Wiley, New York, 1994. |
| [5] |
A. Eden, B. Michaux and J.-M. Rakotoson, Doubly nonlinear parabolic-type equations as dynamical systems, J. Dyn. Diff. Eqns., 3 (1991), 87-131.
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), 321-339.
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), 178-192.
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 "Translations of Mathematical Monographs," Vol. 23, American Mathematical Society, Providence, R.I., 1967. |
| [9] |
J. Málek and D. Prážak, Large time behavior via the method of $l$-trajectories, J. Diff. Eqns., 181 (2002), 243-279.
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), 163-182.
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), 1773-1797.
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), 281-294.
doi: doi:10.1016/j.jmaa.2007.06.028. |
| [13] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Springer, New York, 1988. |
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