Global Attractor for a Class of Parabolic Equations with Infinite Delay

• Autorzy: Anh C. T. , Hieu L. V. , Thanh D. T. P.

Identyfikatory

DOI

10.4064/ba62-1-6

• Języki publikacji: EN

Abstrakty

EN

We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.

Słowa kluczowe

EN

infinite delay; sectorial operator; mild solution; global attractor

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no 1
• Strony: 49--60
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Anh C. T.

• Department of Mathematics Hanoi University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam

autor

Hieu L. V.

• Academy of Journalism and Communication 36 Xuan Thuy, Cau Giay Hanoi, Vietnam

autor

Thanh D. T. P.

• Department of Mathematics Hung Vuong University Nong Trang, Viet Tri Phu Tho, Vietnam

Bibliografia

• [1] M. Adimy, H. Bouzahir and K. Ezzinbi, Existence for a class of partial functional differential equations with infinite delay, Nonlinear Anal. 46 (2001), 91-112.
• [2] M. Adimy, H. Bouzahir and K. Ezzinbi, Local existence and stability for some partial functional differential equations with infinite delay, Nonlinear Anal. 48 (2002), 323-348.
• [3] C. T. Anh and L. V. Hieu, Existence and uniform asymptotic stability for parabolic equations with infinite delay, Electron. J. Differential Equations 2011, no. 51, 14 pp.
• [4] C. T. Anh and L. V. Hieu, Attractors for non-autonomous semilinear parabolic equations with delays, Acta Math. Vietnam. 37 (2012), 357-377.
• [5] R. Benkhalti and K. Ezzinbi, Existence and stability in the α-norm for some partial functional differential equations with infinite delay, Differential Integral Equations 19 (2006), 545-572.
• [6] H. Bouzahir and K. Ezzinbi, Global attractor for a class of partial functional differential equations with infinite delay, in: T. Faria et al. (eds.), Topics in Functional Difference Equations (Lisbon, 1999), Fields Inst. Comm. 29, Amer. Math. Soc., Providence, RI, 1999, 63-71.
• [7] H. Bouzahir, H. You and R. Yuan, Global attractor for some partial functional differential equations with infinite delay, Funkcial. Ekvac. 54 (2011), 139-156.
• [8] I. D. Chueshov, Introduction to the Theory of Infinite-Dimensional Dissipative Systems, Akta, Kharkiv, 1999 (in Russian). 60 C. T. Anh et al.
• [9] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, 1993.
• [10] A. Elazzouzi and A. Ouhinou, Optimal regularity and stability analysis in the α-norm for a class of partial functional differential equations with infinite delay, Discrete Contin. Dynam. Systems 30 (2011), 115-135.
• [11] E. Hernández and H. Henríquez, Existence of periodic solutions of partial neutral functional-differential equations with unbounded delay, J. Math. Anal. Appl. 221 (1998), 499-522.
• [12] Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay, Lecture Notes in Math. 1473, Springer, Berlin, 1991.
• [13] J. Li and J. Huang, Uniform attractors for non-autonomous parabolic equations with delays, Nonlinear Anal. 71 (2009), 2194-2209.
• [14] X. Li and Z. Li, The asymptotic behavior of the strong solutions for a non-autonomous non-local PDE model with delay, Nonlinear Anal. 72 (2010), 3681-3694.
• [15] X. Li and Z. Li, The global attractor of a non-local PDE model with delay for population dynamics in Rn, Acta Math. Sinica (English Ser.) 27 (2011), 1121-1136.
• [16] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983.
• [17] A. V. Rezounenko and J. Wu, A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors, J. Comput. Appl. Math. 190(2006), 99-113.
• [18] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd ed., Springer, 1997.
• [19] C. C. Travis and G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395-418.
• [20] C. C. Travis and G. F. Webb, Existence, stability and compactness in the α-norm for partial functional differential equations, Trans. Amer. Math. Soc. 240 (1978), 129-143.
• [21] J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer, 1996.
• [22] H. You and R. Yuan, Global attractor for some partial differential equations with finite delay, Nonlinear Anal. 72 (2010), 3566-3574.