Non - autonomous inhomogeneous boundary cauchy problems and retarded equations

• Filali, M. ^[1] ; Moussi, M. ^[1]
  1. [1] University Mohamed.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 22, Nº. 2, 2003, págs. 145-159
• Idioma: inglés
• DOI: 10.4067/S0716-09172003000200005
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• Resumen

  • In this paper we prove the existence and the uniqueness of the classical solution of non-autonomous inhomogeneous boundary Cauchy problems, and that this solution is given by a variation of constants formula. This result is applied to show the existence of solutions of a retarded equation.

• Referencias bibliográficas
  • Citas [1] K. J. Engel and R. Nagel: One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics 194, SpringerVerlag...
  • [2] G. Greiner: Perturbing the boundary conditions of a generator, Houston J. Math. 13, pp. 213-229, (1987).
  • [3] G. Greiner: Semilinear boundary conditions for evolution equations of hyperbolic type, Lecture Notes in Pure and Appl. Math. 116 Dekker,...
  • [4] R. Grimmer and E. Sinestrari: Maximum norm in one-dimensional hyperbolic problems, Diff. Integ. Equat. 5, pp. 421-432, (1992).
  • [5] T. Kato: Linear evolution equations of ”hyperbolic” type, J. Fac. Sci. Tokyo, 17, pp. 241-258, (1970).
  • [6] H. Kellermann: Linear evolution equations with time dependent domain, Semesterbericht Funktionalanalysis T¨ubingen, Wintersemester, pp....
  • [7] N. T. Lan: On nonautonomous Functional Differential Equations, J. Math. Anal. Appl. 239, pp. 158-174, (1999).
  • [8] N. T. Lan and G. Nickel: Time-Dependent operator matrices and inhomogeneous Cauchy Problems, Rend. Circ. Mat. Palermo XLVII, pp. 5-24,...
  • [9] R. Nagel and E. Sinestrari: Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, Marcel Dekker, Lecture Notes...
  • [10] A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, New York Springer (1983).
  • [11] N. Tanaka: Quasilinear evolution equations with non-densely defined operators, Diff. Int. Eq. 9, pp. 1067-1106, (1996).