Existence of Pseudo Almost Automorphic Solutions to a Nonautonomous Heat Equation

• Toka Diagana ^[1]
  1. [1] Howard University

     Howard University

     Estados Unidos

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 13, Nº. 1, 2011, págs. 73-101
• Idioma: inglés
• DOI: 10.4067/S0719-06462011000100006
• Enlaces
  • Texto completo
• Resumen
  • español

    En este trabajo, al hacer algunos supuestos adecuados, se obtiene la existencia de pseudo soluciones automorfas a una ecuacin del calor no autnoma con coeficientes degradados.

  • English

    In this paper, upon making some suitable assumptions, we obtain the existence of pseudo-almost automorphic solutions to a nonautonomous heat equation with gradient coefficients.

• Referencias bibliográficas
  • Acquistapace, P. (1988). Evolution operators and strong solutions of abstract linear parabolic equations. Differential Integral Equations....
  • 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. Rend. Sem. Mat. Univ. Padova....
  • Amann, H. (1995). Linear and Quasilinear Parabolic Problems. Birkhäuser. Berlin.
  • Amir, B,Maniar, L. (2000). Existence and some asymptotic behaviors of solutions to semilinear Cauchy problems with non dense domain via extrapolation...
  • Amir, B,Maniar, L. (1999). Composition of Pseudo-Almost Periodic Functions and Cauchy Problems with Perator of Nondense Domain. Ann. Math....
  • Baroun, M,Boulite, S,Diagana, T,Maniar, L. (2009). Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations....
  • Bochner, S. (1964). Continuous mappings of almost automorphic and almost periodic functions. Proc. Nat. Acad. Sci. USA. 52. 907-910
  • Baroun, M,Boulite, S,N’Guérékata, G. M,Maniar, L. (2008). Almost automorphy of Semilinear Parabolic Equations. J. Differential Equations....
  • Boulite, S,Maniar, L,N’Guérékata, G. M. (2005). Almost Automorphic Solutions for Hyperbolic Semilniear Evolution Equations. Semigroup Forum.....
  • Bugajewski, D,Diagana, T. (2006). Almost Automorphy of the Convolution Operator and Applications to Differential and Functional-Differential...
  • Bugajewski, D,Diagana, T,Mahop, C. M. (2006). Asymptotic and Pseudo Almost Periodicity of the Convolution Operator and Applications to Differential...
  • Cieutat, P,Ezzinbi, K. (2009). Existence, uniqueness and attractiveness of a pseudo almost automorphic solutions for some dissipative differential...
  • Da Prato, G,Grisvard, P. (1979). Equations d’évolution abstraites non linéaires de type parabolique. Ann. Mat. Pura Appl. 4. 329-396
  • Diagana, T. (2007). Stepanov-like pseudo almost periodic functions and their applications to differential equations, Commun. Math. Anal. 3....
  • Diagana, T. (2008). Stepanov-like pseudo almost periodicity and its applications to some nonautonmous differential Equations. Nonlinear Anal....
  • Diagana, T. (2009). Existence of pseudo-almost automorphic solutions to some abstract differential equations with Sp-pseudo-almost automorphic...
  • Diagana, T. (2007). Pseudo almost periodic functions in Banach spaces. Nova Science Publishers, Inc. New York.
  • Diagana, T,Hernández M, E. (2007). Existence and Uniqueness of Pseudo Almost Periodic Solutions to Some Abstract Partial Neutral Functional-Differential...
  • Diagana, T. (2007). Existence and Uniqueness of Pseudo Almost Periodic Solutions to Some Classes of Partial Evolution Equations. Nonlinear...
  • Diagana, T,N’Guérékata, G. M. (2006). Pseudo Almost Periodic Mild Solutions To Hyperbolic Evolution Equationa in Abstract Intermediate Banach...
  • Diagana, T,Henríquez, N,Hernández, E. (2008). Almost automorphic mild solutions to some partial neutral functional-differential Equations...
  • Diagana, T,N’Guérékata, G. M. (2007). Almost automorphic solutions to some classes of partial evolution equations. Appl. Math. Lett. 20. 462-466
  • Engel, K. J,Nagel, R. (1999). One Parameter Semigroups for Linear Evolution Equations. Graduate texts in Mathematics, Springer Verlag.
  • Ezzinbi,Fatajou, S,NGuérékata, G. M. (2009). Pseudo almost automorphic solutions to some neutral partial functional differential equations...
  • Ezzinbi, K,Fatajou, S,NGuérékata, G. M. (2009). Pseudo almost automorphic solutions for dissipative differential equations in Banach spaces....
  • Fink, A. M. (1974). Almost Periodic Differential Equations: Lecture Notes in Mathematics. Springer-Verlag. New York-Berlin.
  • Hernández, E,Henríquez, H. R. (1998). Existence of Periodic Solutions of Partial neutral Functional Differential Equations with Unbounded...
  • Hernández, E. (2004). Existence Results for Partial Neutral Integro-differential Equations with Unbounded Delay. J. Math. Anal. Appl. 292....
  • Hernández M, E,Pelicer, M. L,dos Santos, J. P. C. (2004). Asymptotically Almost Periodic and Almost Periodic Solutions for a Class of Evolution...
  • Hino, Y,Naito, T,Minh, N. V,Shin, J. S. (2002). Almost Periodic Solutions of Differential Equations in Banach Spaces. Stability and Control:...
  • Lions, J.-L,Peetre, J. (1964). Sur une classe d’espaces d’interpolation. Inst. Hautes tudes Sci. Publ. Math. 19. 5-68
  • Lunardi, A. (1995). Analytic Semigroups and Optimal Regularity in Parabolic Problems. PNLDEBirkhäauser Verlag. Basel.
  • Liang, J,Zhang, J,Xiao, T-J. (2008). Composition of Pseudo Almost Automorphic and Asymptotically almost automorphic functions. J. Math. Anal....
  • Liang, J,N’Guérékata, G. M,Xiao, T-J,Zhang, J. (2009). Some properties of pseudo almost automorphic functions and applications to abstract...
  • Maniar, L,Schnaubelt, R. (2003). Almost periodicity of inhomogeneous parabolic evolution equations. Lecture Notes in Pure and Appl. Math....
  • Naso, M. G,Benabdallah, A. (2002). Thermoelastic plate with thermal interior control, Mathematical models and methods for smart materials...
  • N’Guérékata, G. M. (2001). Almost automorphic functions and almost periodic functions in abstract spaces. Kluwer Academic / Plenum Publishers....
  • N’Guérékata, G. M. (2005). Topics in almost automorphy. Springer. New york, Boston, Dordrecht, Lodon, Moscow.
  • N’Guérékata, G. M,Pankov, A. (2008). Stepanov-like almost automorphic functions and monotone evolution equations. Nonlinear Anal. 68. 2658-2667
  • Pankov, A. (1990). Bounded and almost periodic solutions of nonlinear operator differential equations. Kluwer. Dordrecht.
  • 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.
  • Schnaubelt, R. (1999). Sufficient conditions for exponential stability and dichotomy of evolution equations. Forum Math. 11. 543-566
  • Schnaubelt, R. (2001). Asymptotically autonomous parabolic evolution equations. J. Evol. Equ. 1. 19-37
  • Schnaubelt, R. (2004). Functional Analytic Methods for Evolution Equations, in: Lecture Notes in Math. Springer-Verlag. Berlin.
  • Xiao, T-J,Liang, J,Zhang, J. (2008). Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces. Semigroup...
  • Xiao, Ti-J,Zhu, X-X,Liang, J. (2009). Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications. Nonlinear...
  • Yagi, A. (1990). Parabolic equations in which the coefficients are generators of infinitely differentiable semigroups II, Funkcial. Ekvac.....
  • Yagi, A. (1991). Abstract quasilinear evolution equations of parabolic type in Banach spaces, Boll. Un. Mat. Ital. B. 7. 341-368
  • Zaidman, S. Topics in Abstract Differential Equations, Pitman Research Notes in Mathematics Ser. II. John Wiley and Sons. New York.