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Time dependent perturbation in a non-autonomous non-classical parabolic equation
1. | Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, Spain |
References:
[1] |
A. B. Babin and M. I. Vishik, "Attractors of Evolution Equations,'' North-Holland, Amsterdam, 1992. |
[2] |
T. Caraballo, A. N. Carvalho, J. A. Langa and F. Rivero, Existence of pullback attractors for pullback asymptotically compact processes, Nonlinear Analysis, 72 (2010), 1967-1976.
doi: 10.1016/j.na.2009.09.037. |
[3] |
T. Caraballo, A. N. Carvalho, J. A. Langa and F. Rivero, A gradient-like non-autonomous evolution processes, Int. Journal of Bifurcation and Chaos, 20 (2010), 2751-2760.
doi: 10.1142/S0218127410027337. |
[4] |
T. Caraballo, A. N. Carvalho, J. A. Langa and F. Rivero, A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor, Nonlinear Analysis, 74 (2011), 2272-2283.
doi: 10.1016/j.na.2010.11.032. |
[5] |
A. N. Carvallo and J. W. Cholewa, Local well possed, asymptotic behaviour and asymptotic bootstrapping for a class of semilinear evolution equations of the second order in time, Trans. Amer. Math. Soc., 361 (2009), 2567-2586.
doi: 10.1090/S0002-9947-08-04789-2. |
[6] |
A. N. Carvalho and J. A. Langa, An extension of the concept of gradient systems which is stable under perturbation, J. Differential Equations, 246 (2009), 2646-2668.
doi: 10.1016/j.jde.2009.01.007. |
[7] |
A. N. Carvalho and J. A. Langa, Non-autonomous perturbation of autonomous semilinear differential equations: Continuity of local stable and unstable manifolds, J. Differential Equations, 233 (2007), 622-653.
doi: 10.1016/j.jde.2006.08.009. |
[8] |
A. N. Carvalho, J. A. Langa and J. C. Robinson, Lower semicontinuity of attractors for non-autonomous dynamical systems, Ergod. Th. & Dynam. Systems, 29 (2009), 1765-1780.
doi: 10.1017/S0143385708000850. |
[9] |
A. N. Carvalho, J. A. Langa, J. C. Robinson and A. Suárez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations, 236 (2007), 570-603.
doi: 10.1016/j.jde.2007.01.017. |
[10] |
V. V. Chepyzhov and M. I. Vishik, "Attractors for Equations of Mathematical Physics,'' Colloquium Publications 49. American Mathematical Society, 2002. |
[11] |
J. K. Hale, "Asymptotic Behavior of Dissipative System,'' Mathematical Surveys and Monographs vol. 25, 1989. |
[12] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,'' Springer-Verlag, Berlin-New York, 1981. |
[13] |
P. E. Kloeden and M. Rasmussen, "Nonautonomous Dynamical System,'' Mathematical Surveys and Monographs vol. 176, 2011. |
[14] |
O. Ladyzhenskaya, "Attractors for Semigroups and Evolution Equations,'' Lezioni Lincee. [Lincei Lectures], Cambridge University Press, Cambridge, 1991. |
[15] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,'' Springer-Verlag, New York, 1983. |
[16] |
J. C. Robinson, "Infinite-Dimensional Dynamical System. An introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors,'' Cambridge Text in Applied Mathematics, Cambridge, 2001. |
[17] |
G. R. Sell and Y. You, "Dynamics of Evolutionary Equations,'' Applied Mathematical Sciences, 143. Springer-Verlag, New York, 2002. |
[18] |
Ch. Sun, S. Wang and Ch. Zhong, Global attractors for a nonclassical diffusion equation, Acta Math. Sin. (Engl. Ser.), 23 (2007), 1271-1280. |
[19] |
P. E. Sobolevskiĭ, Equations of parabolic type in a Banach space, Trudy Moskov. Mat. Obšč, 10 (1961), 297-350. |
[20] |
R. Temam, "Infinite-Dimensional Dynamical System in Mechanics and Physics,'' Applied Mathematical Sciences 68, Springer-Verlag, New-York, 1988. |
[21] |
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. |
show all references
References:
[1] |
A. B. Babin and M. I. Vishik, "Attractors of Evolution Equations,'' North-Holland, Amsterdam, 1992. |
[2] |
T. Caraballo, A. N. Carvalho, J. A. Langa and F. Rivero, Existence of pullback attractors for pullback asymptotically compact processes, Nonlinear Analysis, 72 (2010), 1967-1976.
doi: 10.1016/j.na.2009.09.037. |
[3] |
T. Caraballo, A. N. Carvalho, J. A. Langa and F. Rivero, A gradient-like non-autonomous evolution processes, Int. Journal of Bifurcation and Chaos, 20 (2010), 2751-2760.
doi: 10.1142/S0218127410027337. |
[4] |
T. Caraballo, A. N. Carvalho, J. A. Langa and F. Rivero, A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor, Nonlinear Analysis, 74 (2011), 2272-2283.
doi: 10.1016/j.na.2010.11.032. |
[5] |
A. N. Carvallo and J. W. Cholewa, Local well possed, asymptotic behaviour and asymptotic bootstrapping for a class of semilinear evolution equations of the second order in time, Trans. Amer. Math. Soc., 361 (2009), 2567-2586.
doi: 10.1090/S0002-9947-08-04789-2. |
[6] |
A. N. Carvalho and J. A. Langa, An extension of the concept of gradient systems which is stable under perturbation, J. Differential Equations, 246 (2009), 2646-2668.
doi: 10.1016/j.jde.2009.01.007. |
[7] |
A. N. Carvalho and J. A. Langa, Non-autonomous perturbation of autonomous semilinear differential equations: Continuity of local stable and unstable manifolds, J. Differential Equations, 233 (2007), 622-653.
doi: 10.1016/j.jde.2006.08.009. |
[8] |
A. N. Carvalho, J. A. Langa and J. C. Robinson, Lower semicontinuity of attractors for non-autonomous dynamical systems, Ergod. Th. & Dynam. Systems, 29 (2009), 1765-1780.
doi: 10.1017/S0143385708000850. |
[9] |
A. N. Carvalho, J. A. Langa, J. C. Robinson and A. Suárez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations, 236 (2007), 570-603.
doi: 10.1016/j.jde.2007.01.017. |
[10] |
V. V. Chepyzhov and M. I. Vishik, "Attractors for Equations of Mathematical Physics,'' Colloquium Publications 49. American Mathematical Society, 2002. |
[11] |
J. K. Hale, "Asymptotic Behavior of Dissipative System,'' Mathematical Surveys and Monographs vol. 25, 1989. |
[12] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,'' Springer-Verlag, Berlin-New York, 1981. |
[13] |
P. E. Kloeden and M. Rasmussen, "Nonautonomous Dynamical System,'' Mathematical Surveys and Monographs vol. 176, 2011. |
[14] |
O. Ladyzhenskaya, "Attractors for Semigroups and Evolution Equations,'' Lezioni Lincee. [Lincei Lectures], Cambridge University Press, Cambridge, 1991. |
[15] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,'' Springer-Verlag, New York, 1983. |
[16] |
J. C. Robinson, "Infinite-Dimensional Dynamical System. An introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors,'' Cambridge Text in Applied Mathematics, Cambridge, 2001. |
[17] |
G. R. Sell and Y. You, "Dynamics of Evolutionary Equations,'' Applied Mathematical Sciences, 143. Springer-Verlag, New York, 2002. |
[18] |
Ch. Sun, S. Wang and Ch. Zhong, Global attractors for a nonclassical diffusion equation, Acta Math. Sin. (Engl. Ser.), 23 (2007), 1271-1280. |
[19] |
P. E. Sobolevskiĭ, Equations of parabolic type in a Banach space, Trudy Moskov. Mat. Obšč, 10 (1961), 297-350. |
[20] |
R. Temam, "Infinite-Dimensional Dynamical System in Mechanics and Physics,'' Applied Mathematical Sciences 68, Springer-Verlag, New-York, 1988. |
[21] |
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. |
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