- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 183420, 10 pages
Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain
1Department of Mathematics, North University of China, Taiyuan 030051, China
2School of Mechatronic Engineering, North University of China, Taiyuan 030051, China
Received 5 March 2013; Accepted 22 April 2013
Academic Editor: Yonghui Xia
Copyright © 2013 Zhanrong Hu and Zhen Jin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- S. Bochner, “A new approach to almost periodicity,” Proceedings of the National Academy of Sciences of the United States of America, vol. 48, pp. 2039–2043, 1962.
- W. A. Veech, “Almost automorphic functions on groups,” American Journal of Mathematics, vol. 87, pp. 719–751, 1965.
- W. A. Veech, “On a theorem of Bochner,” Annals of Mathematics, vol. 86, pp. 117–137, 1967.
- M. Zaki, “Almost automorphic solutions of certain abstract differential equations,” Annali di Matematica Pura ed Applicata, vol. 101, pp. 91–114, 1974.
- W. Shen and Y. Yi, “Almost automorphic and almost periodic dynamics in skew-product semi ows,” Memoirs of the American Mathematical Society, vol. 136, no. 647, 1998.
- G. M. N'Guérékata, Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces, Kluwer Academic/Plenum, New York, NY, USA, 2001.
- G. M. N'Guérékata, Topics in Almost Automorphy, Springer, New York, NY, USA, 2005.
- S. Boulite, L. Maniar, and G. M. N'Guérékata, “Almost automorphic solutions for hyperbolic semilinear evolution equations,” Semigroup Forum, vol. 71, no. 2, pp. 231–240, 2005.
- P. Cieutat and K. Ezzinbi, “Almost automorphic solutions for some evolution equations through the minimizing for some subvariant functional, applications to heat and wave equations with nonlinearities,” Journal of Functional Analysis, vol. 260, no. 9, pp. 2598–2634, 2011.
- T. Diagana, G. Nguerekata, and Nguyen Van Minh, “Almost automorphic solutions of evolution equations,” Proceedings of the American Mathematical Society, vol. 132, no. 11, pp. 3289–3298, 2004.
- J. A. Goldstein and G. M. N'Guérékata, “Almost automorphic solutions of semilinear evolution equations,” Proceedings of the American Mathematical Society, vol. 133, no. 8, pp. 2401–2408, 2005.
- G. M. N'guerekata, “Almost automorphy, almost periodicity and stability of motions in Banach spaces,” Forum Mathematicum, vol. 13, no. 4, pp. 581–588, 2001.
- G. M. N'Guérékata, “Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations,” Semigroup Forum, vol. 69, no. 1, pp. 80–86, 2004.
- M. Baroun, S. Boulite, G. M. N'Guérékata, and L. Maniar, “Almost automorphy of semilinear parabolic evolution equations,” Electronic Journal of Differential Equations, vol. 2008, pp. 1–9, 2008.
- H.-S. Ding, W. Long, and G. M. N'Guérékata, “Almost automorphic solutions of nonautonomous evolution equations,” Nonlinear Analysis. Theory, Methods & Applications A: Theory and Methods, vol. 70, no. 12, pp. 4158–4164, 2009.
- J.-H. Liu and X.-Q. Song, “Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations,” Journal of Functional Analysis, vol. 258, no. 1, pp. 196–207, 2010.
- M. Adimy and K. Ezzinbi, “A class of linear partial neutral functional-differential equations with nondense domain,” Journal of Differential Equations, vol. 147, no. 2, pp. 285–332, 1998.
- G. Da Prato and E. Sinestrari, “Differential operators with nondense domain,” Annali della Scuola Normale Superiore di Pisa, vol. 14, no. 2, pp. 285–344, 1987.
- E. Sinestrari, “On the abstract Cauchy problem of parabolic type in spaces of continuous functions,” Journal of Mathematical Analysis and Applications, vol. 107, no. 1, pp. 16–66, 1985.
- L. Maniar and R. Schnaubelt, “Almost periodicity of inhomogeneous parabolic evolution equations,” in Lecture Notes in Pure and Applied Mathematics, vol. 234, pp. 299–318, Dekker, New York, NY, USA, 2003.
- R. Schnaubelt, “Asymptotic behaviour of parabolic nonautonomous evolution equations,” in Functional Analytic Methods for Evolution Equations, vol. 1855 of Lecture Notes in Mathematics, pp. 401–472, Springer, Berlin, Germany, 2004.
- C. Chicone and Y. Latushkin, Evolution Semigroups in Dynamical systems and Differential Equations, American Mathematical Society, Providence, RI, USA, 1999.
- W. A. Coppel, Dichotomies in Stability Theory, Springer, Berlin, Germany, 1978.
- R. J. Sacker and G. R. Sell, “Dichotomies for linear evolutionary equations in Banach spaces,” Journal of Differential Equations, vol. 113, no. 1, pp. 17–67, 1994.
- H.-S. Ding, J. Liang, and T.-J. Xiao, “Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications Series A: Theory and Methods, vol. 73, no. 5, pp. 1426–1438, 2010.
- T.-J. Xiao, X.-X. Zhu, and J. Liang, “Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications,” Nonlinear Analysis. Theory, Methods & Applications. A: Theory and Methods, vol. 70, no. 11, pp. 4079–4085, 2009.
- P. Acquistapace and B. Terreni, “A unified approach to abstract linear nonautonomous parabolic equations,” Rendiconti del Seminario Matematico della Università di Padova, vol. 78, pp. 47–107, 1987.
- P. Acquistapace, “Evolution operators and strong solutions of abstract linear parabolic equations,” Differential and Integral Equations, vol. 1, no. 4, pp. 433–457, 1988.
- A. Yagi, “Parabolic evolution equations in which the coefficients are the generators of infinitely differentiable semigroups. II,” Funkcialaj Ekvacioj, vol. 33, no. 1, pp. 139–150, 1990.
- A. Yagi, “Abstract quasilinear evolution equations of parabolic type in Banach spaces,” Unione Matematica Italiana B, vol. 5, no. 2, pp. 341–368, 1991.
- H. Amann, Linear and Quasilinear Parabolic Problems. Volume 1: Abstract Linear Theory, Birkhäuser Boston, Boston, Mass, USA, 1995.
- A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, Switzerland, 1995.