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Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions to Some Evolution Equations Involving Theoretical Measure Theory

  • Toka Diagana [1] ; Khalil Ezzinbi [2] ; Mohsen Miraoui [3]
    1. [1] Howard University
    2. [2] Université Cadi Ayyad Faculté des Sciences Semlalia Département de Mathématiques
    3. [3] Institut supérieur des Etudes technologiques de Kairouan, Rakkada
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  • Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 16, Nº. 2, 2014, págs. 1-32
  • Idioma: inglés
  • DOI: 10.4067/S0719-06462014000200001
  • Enlaces
  • Resumen
    • español

      Motivado por los trabajos recientes del primer y segundo autor, en este artículo introducimos la noción de seudo-casi periodicidad con doble peso (seudo-casi automorfía con doble peso respectivamente) usando Teoría de la Medida. Se estudian las propiedades básicas de estos espacios nuevos. Para ilustrar nuestro trabajo, bajo las condiciones de Acquistapace-Terreni y dicotomía exponencial estudiamos la existencia de soluciones (respectivamente, seudo-casi periódicas seudo-casi automórficas) para algunas ecuaciones parciales de evolución autónomas en espacios de Banach. Algunos ejemplos ilustrativos se discutirán al final del artículo.

    • English

      Motivated by the recent works by the first and the second named authors, in this paper we introduce the notion of doubly-weighted pseudo-almost periodicity (respectively, doubly-weighted pseudo-almost automorphy) using theoretical measure theory. Basic properties of these new spaces are studied. To illustrate our work, we study, under Acquistapace-Terreni conditions and exponential dichotomy, the existence of - pseudo almost periodic (respectively-pseudo almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces. A few illustrative examples will be discussed at the end of the paper.

  • Referencias bibliográficas
    • Acquistapace, P,Flandoli, F,Terreni, B. (1991). Initial boundary value problems and optimal control for nonautonomous parabolic systems. SIAM...
    • Acquistapace, P,Terreni, B. (1987). A unified approach to abstract linear nonautonomous parabolic equations. Rendiconti del Seminario Matematico...
    • Ait Dads, E,Cieutat, P,Ezzinbi, K. The existence of pseudo-almost periodic solutions for some nonlinear differential equations in Banach spaces...
    • Ait Dads, E,Ezzinbi, K,Arino, O. (1997). Pseudo almost periodic solutions for some differential equations in Banach space. Nonlinear Analysis...
    • Ait Dads, E,Ezzinbi, K. (1996). Pseudo almost periodic solutions of some delay differential equations. Journal of Mathematical Analysis and...
    • Amann, H. (1995). Linear and Quasilinear Parabolic Problems. Birkhäuser. Berlin.
    • Amir, B,Maniar, L. (1999). Composition of pseudo-almost periodic functions and cauchy problems with perator of nondense domain. Annales Mathématiques...
    • Baroun, M,Boulite, S,Diagana, T,Maniar, L. (2009). Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations....
    • Baroun, M,Boulite, S,N’Guérékata, G. M,Maniar, L. (2008). Almost automorphy of semilinear parabolic evolution equations. Electronic Journal...
    • Batty, C. J. K,Hutter, W,Räbiger, F. (1999). Almost periodicity of mild solutions of inhomogeneous Cauchy problems. Journal Differential Equations....
    • Blot, J,Mophou, G. M,N’Guérékata, G. M,Pennequin, D. (2009). Weighted pseudo-almost automorphic functions and applications to abstract differential...
    • Blot, J,Cieutat, P,Ezzinbi, K. (2011). New approach for weighted pseudo-almost periodic functions under the light of measure theory: basic...
    • Blot, J,Cieutat, P,Ezzinbi, K. (2012). Measure theory and pseudo almost automorphic functions: New developments and applications. Nonlinear...
    • Bochner, S. (1964). Continuous mappings of almost automorphic and almost periodic functions. Proceedings of the National Academy of Sciences...
    • Bohr, H. (1947). Almost periodic functions. Chelsea Publishing Company. New York.
    • Boukli-Hacene, N,Ezzinbi, K. Weighted pseudo almost periodic solutions for some partial functional differential equations Nonlinear Analysis:...
    • Boukli-Hacene, N,Ezzinbi, K. (2010). Weighted pseudo-almost automorphic solutions for partial functional differential equations. Nonlinear...
    • Boulite, S,Maniar, L,N’Guérékata, G. M. (2005). Almost automorphic solutions for hyperbolic semilinear evolution equations. Semigroup Forum....
    • Chang, Y-K,Zhao, Z-H,Nieto, J.J. (2011). Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to semi-linear differential...
    • Cieutat, P,Fatajou, S,N’Guérékata, G.M. (2010). Composition of pseudo almost periodic and pseudo almost automorphic functions and applications...
    • Corduneanu, C. (1968). Almost Periodic Functions. WileyChelsea. New YorkNew York.
    • Diagana, T,N’Guérékata, G,Van Minh, N. (2004). Almost automorphic solutions of evolution equations. Proc. Amer. Math. Soc. 132. 3289-3298
    • Diagana, T,Mahop, C.M,N’Guérékata, G.M,Toni, B. (2006). Existence and uniqueness of pseudo-almost periodic solutions to some classes of semilinear...
    • Diagana, T. (2007). Existence and uniqueness of pseudo-almost periodic solutions to some classes of partial evolution equations. Nonlinear...
    • Diagana, T. (2009). Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations. Journal of Mathematical...
    • Diagana, T. (2011). Existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations. Nonlinear...
    • Diagana, T. (2007). Pseudo Almost Periodic Functions in Banach Spaces. Nova Science Publishers, Inc. New York.
    • Diagana, T. (2005). Pseudo almost periodic solutions to some differential equations. Nonlinear Analysis Theory Methods Appl. 60. 1277-1286
    • Diagana, T. (2006). Weighted pseudo almost periodic functions and applications. C.R.A.S. 343. 643-646
    • Diagana, T. (2011). Doubly-weighted pseudo almost periodic functions. Afr. Diaspora J. Math. 12. 121-136
    • Diagana, T. (2008). Weighted pseudo-almost periodic solutions to some differential equations. Nonlinear Analysis. 68. 2250-2260
    • Diagana, T. (2009). Pseudo-almost automorphic solutions to some classes of nonautonomous partial evolution equations. Differential Equations...
    • Diagana, T. (2011). Pseudo-almost periodic solutions for some classes of nonautonomous partial evolution equations. Journal of the Franklin...
    • Engel, K. J,Nagel, R. (1999). One Parameter Semigroups for Linear Evolution Equations. Springer Verlag.
    • Ezzinbi, K,N’Guérékata, G.M. (2007). Almost automorphic solutions for some partial functional differential equations. Journal of Mathematical...
    • Ezzinbi, K,N’Guérékata, G.M. (2007). Almost automorphic solutions for some partial functional differential equations. Journal of Mathematical...
    • Ezzinbi, K,Nelson, V,N’Guérékata, G.M. (2008). C(n)-almost automorphic solutions of some nonautonomous differential equations. Cubo. 10. 61-74
    • Fréchet, M. (1941). Sur le théorème ergodique de Birkhoff. Les Comptes Rendus Mathématique de l’Académie des sciences Paris. 213. 607-609
    • Goldstein, J.A,N’Guérékata, G.M. (2005). Almost automorphic solutions of semilinear evolution equations. Proceedings of the America Mathematical...
    • Gühring, G,Räbiger, F. (1999). Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded...
    • Gühring, G,Räbiger, F,Schnaubelt, R. (2002). A characteristic equation for nonautonomous partial functional differential equations. Journal...
    • Hino, Y,Murakami, S. (2003). Almost automorphic solutions for abstract functional differential equations. Journal of Mathematical Analysis...
    • Liang, J,Xiao, T.J,Zhang, J. (2010). Decomposition of weighted pseudo-almost periodic functions. Nonlinear Analysis Theory Methods Appl. 73....
    • Liang, J,N’Guérékata, G.M,Xiao, T-J,Zhang, J. (2009). Some properties of pseudo-almost automorphic functions and applications to abstract...
    • Liang, J,Zhang, J,Xiao, T-J. (2008). Composition of pseudo almost automorphic and asymptotically almost automorphic functions. Journal of...
    • Liang, J,Xiao, T-J,Zhang, J. (2010). Decomposition of weighted pseudo-almost periodic functions. Nonlinear Analysis, Theory, Methods and Applications....
    • Liu, J. H,N’Guérékata, G. M,Minh, N. V. (2008). Topics on stability and periodicity in abstract differential equations. 6.
    • Maniar, L,Schnaubelt, R. (2003). Almost periodicity of inhomogeneous parabolic evolution equations, in: Lecture Notes in Pure and Applied...
    • N’Guérékata, G.M. (2001). Almost Automorphic and Almost Periodic Functions in Abstract Spaces. Kluwer Academic Plenum Publishers. New YorkBostonMoscowLondon....
    • N’Guérékata, G.M. (2004). Existence and uniqueness of almost automorphic mild solution to some semilinear abstract differential equations....
    • N’Guérékata, G. M. (2005). Topics in Almost Automorphy. Springer. New YorkBostonDordrechtLondonMoscow.
    • Pazy, A. (1983). Semigroups of linear operators and applications to partial differential equations: Applied Mathematical Sciences. Springer-Verlag....
    • Prüss, J. (1993). Evolutionary Integral Equations and Applications. Birkhäuser.
    • Schwartz, L. (1976). Topologie Generale et Analyse Fonctionnelle. Hermann. Paris.
    • Schnaubelt, R. (1999). Sufficient conditions for exponential stability and dichotomy of evolution equations. Forum Math. 11. 543-566
    • Quôc Phóng, V. (1995). Stability and almost periodicity of trajectories of periodic processes. Journal Differential Equations. 115. 402-415
    • Xiao, T-J,Liang, J,Zhang, J. (2008). Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces. Semigroup...
    • Xiao, T-J,Zhu, X. X,Liang, J. (2009). Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications. Nonlinear...
    • Zhang, C.Y. (1994). Pseudo almost periodic solutions of some differential equations. Journal ofMathematical Analysis and Applications. 151....
    • Zhang, C. (2003). Pseudo Almost Periodic Type Functions and Ergodicity. Science Press, Kluwer Academic Publishers. Dordrecht.
Los metadatos del artículo han sido obtenidos de SciELO Chile
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