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A nonlinear eigenvalue problem for the periodic scalar $p$-Laplacian
Time periodic solutions for a sixth order nonlinear parabolic equation in two space dimensions
| 1. | Department of Mathematics, Jilin University, Changchun 130012, China |
References:
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Y. Fu and B. Guo, Time periodic solution of the viscous Camassa-Holm equation, J. Math. Anal. Appl., 313 (2006), 311-321.
doi: 10.1016/j.jmaa.2005.08.073. |
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C. Liu, Regularity of solutions for a sixth order nonlinear parabolic equation in two space dimensions, Annales Polonici Mathematici, 107 (2013), 271-291.
doi: 10.4064/ap107-3-4. |
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I. Pawłow and W. Zajączkowski, A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures, Commun. Pure Appl. Anal., 10 (2011), 1823-1847.
doi: 10.3934/cpaa.2011.10.1823. |
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G. Schimperna and I. Pawłow, On a class of Cahn-Hilliard models with nonlinear diffusion, SIAM J. Math. Anal., 45 (2013), 31-63.
doi: 10.1137/110835608. |
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R. Wang, The Schauder theory of the boundary value problem for parabolic problem equations, Acta Sci. Nature Univ. Jilin., 2 (1964), 35-64. |
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Y. Wang and Y. Zhang, Time-periodic solutions to a nonlinear parabolic type equation of higher order, Acta Math. Appl. Sin., Engl. Ser., 24 (2008), 129-140.
doi: 10.1007/s10255-006-6174-3. |
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L. Yin, Y. Li, R. Huang and J. Yin, Time periodic solutions for a Cahn-Hilliard type equation, Mathematical and Computer Modelling, 48 (2008), 11-18.
doi: 10.1016/j.mcm.2007.09.001. |
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J. Yin, Y. Li and R. Huang, The Cahn-Hilliard type equations with periodic potentials and sources, Appl. Math. Comput., 211 (2009), 211-221.
doi: 10.1016/j.amc.2009.01.038. |
show all references
References:
| [1] |
Y. Fu and B. Guo, Time periodic solution of the viscous Camassa-Holm equation, J. Math. Anal. Appl., 313 (2006), 311-321.
doi: 10.1016/j.jmaa.2005.08.073. |
| [2] |
M. Giaquinta and M. Struwe, On the partial regularity of weak solutions of nonlinear parabolic systems, Math. Z., 179 (1982), 437-451.
doi: 10.1007/BF01215058. |
| [3] |
G. Gompper and J. Goos, Fluctuating interfaces in microemulsion and sponge phases, Phys. Rev. E, 50 (1994), 1325-1335. |
| [4] |
C. Liu, Regularity of solutions for a sixth order nonlinear parabolic equation in two space dimensions, Annales Polonici Mathematici, 107 (2013), 271-291.
doi: 10.4064/ap107-3-4. |
| [5] |
I. Pawłow and W. Zajączkowski, A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures, Commun. Pure Appl. Anal., 10 (2011), 1823-1847.
doi: 10.3934/cpaa.2011.10.1823. |
| [6] |
G. Schimperna and I. Pawłow, On a class of Cahn-Hilliard models with nonlinear diffusion, SIAM J. Math. Anal., 45 (2013), 31-63.
doi: 10.1137/110835608. |
| [7] |
R. Wang, The Schauder theory of the boundary value problem for parabolic problem equations, Acta Sci. Nature Univ. Jilin., 2 (1964), 35-64. |
| [8] |
Y. Wang and Y. Zhang, Time-periodic solutions to a nonlinear parabolic type equation of higher order, Acta Math. Appl. Sin., Engl. Ser., 24 (2008), 129-140.
doi: 10.1007/s10255-006-6174-3. |
| [9] |
L. Yin, Y. Li, R. Huang and J. Yin, Time periodic solutions for a Cahn-Hilliard type equation, Mathematical and Computer Modelling, 48 (2008), 11-18.
doi: 10.1016/j.mcm.2007.09.001. |
| [10] |
J. Yin, Y. Li and R. Huang, The Cahn-Hilliard type equations with periodic potentials and sources, Appl. Math. Comput., 211 (2009), 211-221.
doi: 10.1016/j.amc.2009.01.038. |
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