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Limits of anisotropic and degenerate elliptic problems
Dynamics of non-autonomous nonclassical diffusion equations on $R^n$
1. | Department of Mathematics, Hanoi National University of Education, 36 Xuan Thuy, Cau Giay, Hanoi, Vietnam |
2. | Faculty of Applied Mathematics and Informatics, Hanoi University of Science and Technology, No 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam |
References:
[1] |
E. C. Aifantis, On the problem of diffusion in solids, Acta Mech., 37 (1980), 265-296.
doi: 10.1007/BF01202949. |
[2] |
C. T. Anh and T. Q. Bao, Pullback attractors for a class of non-autonomous nonclassical diffusion equations, Nonlinear Anal., 73 (2010), 399-412.
doi: 10.1016/j.na.2010.03.031. |
[3] |
A. N. Carvalho, J. A. Langa and J. C. Robinson, On the continuity of pullback attractors for evolution processes, Nonlinear Anal., 71 (2009), 1812-1824.
doi: 10.1016/j.na.2009.01.016. |
[4] |
Y. Li and C. K. Zhong, Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction-diffusion equations, Appl. Math. Comp., 190 (2007), 1020-1029.
doi: 10.1016/j.amc.2006.11.187. |
[5] |
Y. Li, S. Wang and H. Wu, Pullback attractors for non-autonomous reaction-diffusion equations in $L^p$, Appl. Math. Comp., 207 (2009), 373-379.
doi: 10.1016/j.amc.2008.10.065. |
[6] |
J. L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires," Dunod, Paris, 1969. |
[7] |
Q. F. Ma, S. H. Wang and C. K. Zhong, Necessary and sufficient conditions for the existence of global attractor for semigroups and applications, Indian University Math. J., 51 (2002), 1541-1559.
doi: 10.1512/iumj.2002.51.2255. |
[8] |
J. C. Peter and M. E. Gurtin, On a theory of heat conduction involving two temperatures, Z. Angew. Math. Phys., 19 (1968), 614-627.
doi: 10.1007/BF01594969. |
[9] |
C. Sun, S. Wang and C. Zhong, Global attractors for a nonclassical diffusion equation, Acta Math. Appl. Sin., Engl. Ser, 23 (2007), 1271-1280.
doi: 10.1007/s10114-005-0909-6. |
[10] |
C. Sun and M. Yang, Dynamics of the nonclassical diffusion equations, Asymp. Anal., 59 (2009), 51-81.
doi: 10.3233/ASY-2008-0886. |
[11] |
C. Truesdell and W. Noll, "The Nonlinear Field Theories of Mechanics," Encyclomedia of Physics, Springer, Berlin, 1995. |
[12] |
B. Wang, Attractors for reaction-diffusion equations in unbounded domains, Physica D, 179 (1999), 41-52.
doi: 10.1016/S0167-2789(98)00304-2. |
[13] |
B. Wang, Pullback attractors for non-autonomous reaction-diffusion equations on $\mathbb R^n$, Front. Math. China, 4 (2009), 563-583.
doi: 10.1007/s11464-009-0033-5. |
[14] |
S. Wang, D. Li and C. Zhong, On the dynamics of a class of nonclassical parabolic equations, J. Math. Anal. Appl., 317 (2006), 565-582.
doi: 10.1016/j.jmaa.2005.06.094. |
[15] |
Y. Xiao, Attractors for a nonclassical diffusion equation, Acta Math. Appl. Sin., Engl. Ser, 18 (2002), 273-276.
doi: 10.1007/s102550200026. |
[16] |
C. K. Zhong, M. H. Yang and C. Y. Sun, The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations, J. Differential Equations, 15 (2006), 367-399.
doi: 10.1016/j.jde.2005.06.008. |
show all references
References:
[1] |
E. C. Aifantis, On the problem of diffusion in solids, Acta Mech., 37 (1980), 265-296.
doi: 10.1007/BF01202949. |
[2] |
C. T. Anh and T. Q. Bao, Pullback attractors for a class of non-autonomous nonclassical diffusion equations, Nonlinear Anal., 73 (2010), 399-412.
doi: 10.1016/j.na.2010.03.031. |
[3] |
A. N. Carvalho, J. A. Langa and J. C. Robinson, On the continuity of pullback attractors for evolution processes, Nonlinear Anal., 71 (2009), 1812-1824.
doi: 10.1016/j.na.2009.01.016. |
[4] |
Y. Li and C. K. Zhong, Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction-diffusion equations, Appl. Math. Comp., 190 (2007), 1020-1029.
doi: 10.1016/j.amc.2006.11.187. |
[5] |
Y. Li, S. Wang and H. Wu, Pullback attractors for non-autonomous reaction-diffusion equations in $L^p$, Appl. Math. Comp., 207 (2009), 373-379.
doi: 10.1016/j.amc.2008.10.065. |
[6] |
J. L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires," Dunod, Paris, 1969. |
[7] |
Q. F. Ma, S. H. Wang and C. K. Zhong, Necessary and sufficient conditions for the existence of global attractor for semigroups and applications, Indian University Math. J., 51 (2002), 1541-1559.
doi: 10.1512/iumj.2002.51.2255. |
[8] |
J. C. Peter and M. E. Gurtin, On a theory of heat conduction involving two temperatures, Z. Angew. Math. Phys., 19 (1968), 614-627.
doi: 10.1007/BF01594969. |
[9] |
C. Sun, S. Wang and C. Zhong, Global attractors for a nonclassical diffusion equation, Acta Math. Appl. Sin., Engl. Ser, 23 (2007), 1271-1280.
doi: 10.1007/s10114-005-0909-6. |
[10] |
C. Sun and M. Yang, Dynamics of the nonclassical diffusion equations, Asymp. Anal., 59 (2009), 51-81.
doi: 10.3233/ASY-2008-0886. |
[11] |
C. Truesdell and W. Noll, "The Nonlinear Field Theories of Mechanics," Encyclomedia of Physics, Springer, Berlin, 1995. |
[12] |
B. Wang, Attractors for reaction-diffusion equations in unbounded domains, Physica D, 179 (1999), 41-52.
doi: 10.1016/S0167-2789(98)00304-2. |
[13] |
B. Wang, Pullback attractors for non-autonomous reaction-diffusion equations on $\mathbb R^n$, Front. Math. China, 4 (2009), 563-583.
doi: 10.1007/s11464-009-0033-5. |
[14] |
S. Wang, D. Li and C. Zhong, On the dynamics of a class of nonclassical parabolic equations, J. Math. Anal. Appl., 317 (2006), 565-582.
doi: 10.1016/j.jmaa.2005.06.094. |
[15] |
Y. Xiao, Attractors for a nonclassical diffusion equation, Acta Math. Appl. Sin., Engl. Ser, 18 (2002), 273-276.
doi: 10.1007/s102550200026. |
[16] |
C. K. Zhong, M. H. Yang and C. Y. Sun, The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations, J. Differential Equations, 15 (2006), 367-399.
doi: 10.1016/j.jde.2005.06.008. |
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