Existence and stability in the α-norm for nonlinear neutral partial differential equations with finite delay

• Taoufik Chitioui ^[1] ; Khalil Ezzinbi ^[2] ; Amor Rebey ^[3]
  1. [1] University of Sfax

     University of Sfax

     Túnez

     
  2. [2] Cadi Ayyad University

     Cadi Ayyad University

     Marrakech-Medina, Marruecos

     
  3. [3] University of Kairouan

     University of Kairouan

     Túnez

     

  Mostrar afiliaciones +
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 15, Nº. 1, 2013, págs. 49-75
• Idioma: inglés
• DOI: 10.4067/S0719-06462013000100004
• Enlaces
  • Texto completo
• Resumen
  • español

    En este trabajo estudiamos la existencia, regularidad y estabilidad de soluciones para una clase de ecuaciones diferenciales parciales funcionales neutrales. Asumimos que la parte lineal genera un semigrupo compacto analí­tico en un espacio de Banach X, la parte retardada se asume continua respecto de la potencia fraccional del generador. Como ejemplo, se muestra una aplicación para un modelo con difusión y no linealidad en el gradiente.

  • English

    In this work, we study the existence, regularity and stability of solutions for some nonlinear class of partial neutral functional differential equations. We assume that the linear part generates a compact analytic semigroup on a Banach space X, the delayed part is assumed to be continuous with respect to the fractional power of the generator. For illustration, some application is provided for some model with diffusion and nonlinearity in the gradient.

• Referencias bibliográficas
  • Adimy, M,Ezzinbi, K. (1998). A class of linear partial neutral functional dierential equations with non- dense domain. Journal of Differential...
  • Adimy, M,Ezzinbi, K. (1999). Existence and linearized stability for partial neutral functional differential equations with nondense domains....
  • Adimy, M,Ezzinbi, K. (1999). Strict solutions of nonlinear hyperbolic neutral dierential equations. Appl. Math. Letters. 12. 107-112
  • Adimy, M,Ezzinbi, K. (2006). Existence and stability in the α-norm for partial functional differential equations of neutral type. Annali di...
  • Adimy, M,Bouzahir, H,Ezzinbi, K. (2001). Existence for a class of partial functional differential equations with infinite delay. Nonlinear...
  • Adimy, M,Bouzahir, H,Ezzinbi, K. (2002). Local existence and stability for some partial functional differential equations with infinite delay....
  • Adimy, M,Bouzahir, H,Ezzinbi, K. (2004). Existence and stability for some partial neutral functional differential equations with infinite...
  • Adimy, M,Elazzouzi, A,Ezzinbi, K. (2009). Reduction principle and dynamic behaviors for a class of partial functional differential equations....
  • Adimy, M,Ezzinbi, K,Laklach, M. (2000). Existence of solutions for a class of partial neutral differential equations. C. R. Acad. Sci. Paris...
  • Banas, J,Goebel, K. (1980). Measure of Noncompactness in Banach spaces. Marcle Dekker. ^eNew York New York.
  • Muslim, M,Bahuguna, D. (2008). Existence of solutions to neutral differential equations with deviated argument. Electronic Journal of Differential...
  • Changa, J,Liu, H. (2009). Existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α-norm....
  • Desch, W,Schappacher, W. (1986). Differential Equations in Banach Spaces. Springer-Verlag.
  • Engel, K,Nagel, D. (2000). One-parameter Semigroups for Linear Evolution Equations: Graduate Texts in Mathematics. Springer-Verlag.
  • Henry, D. (1989). Geometric Theory of Semilinear Parabolic Partial Differential Equations. Springer-Verlag. Berlin^eNew York New York.
  • Ezzinbi, K,Fu, X,Hilal, K. (2007). Existence and regularity in the α-norm for some neutral partial differential equations with nonlocal conditions....
  • Fu, X,Ezzinbi, K. (2003). Existence of solutions for neutral functional evolution equations with nonlocal conditions. Nonlinear Analinear...
  • Ezzinbi, K,Megdiche, H,Rebey, A. (2010). Existence of solutions in the alpha-norm for partial differential equations of neutral type with...
  • Hale, J. K. (1994). Partial neutral functional differential equations. Rev. Roum. Math. Pures Appl. 39. 339-344
  • Hale, J. K. (1994). Coupled Oscillators on a Circle. Resen. Inst. Mat. Estat. Univ. Sao Paulo. 1. 441-457
  • Hale, J.K,Kato, J. (1978). Phase space for retarded equations with infinite delay. Funkcialaj Ekvacioj. 21. 11-41
  • Hale, J.K,Verduyn-Lunel, S. (1993). Applied Mathematical Sciences. Springer-Verlag. ^eNew York New York.
  • Hino, Y,Murakami, S,Naito, T. (1991). Functional Differential Equations with Infinite Delay: Lectures Notes. Springer-Verlag.
  • Pazy, A. (1983). Semigroups of Linear Operators and Application to Partial Differental Equation. Applied Mathematical Sciences, Springer-Verlag....
  • Sadovskii, B. N. (1967). On a fixed point principle. Functional Analysis and its Applications. 1. 74-76
  • Travis, C. C,Webb, G. F. (1974). Existence and Stability for Partial Functional Differential Equations. Journal of Mathematical Analysis and...
  • Travis, C. C,Webb, G. F. (1978). Existence, stability, and compactness in the α-norm for partial functional differential equations. Transaction...
  • Travis, C. C,Webb, G. F. (1976). Partial differential equations with deviating arguments in the time variable. Transactions of the American...
  • Wu, J. (1996). Theory and Applications for Partial Functional Differential Function. Applied Mathematical Sciences, Springer-Verlag.
  • Wu, J,Xia, H. (1996). Self-sustained oscillations in a ring array of coupled lossless transmission lines. Journal of Differential Equations....