Differentiability of solutions of the abstract cauchy problem

• Henríquez Miranda, Hernán R. ^[1]
  1. [1] Universidad de Santiago.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 20, Nº. 3, 2001, págs. 295-304
• Idioma: inglés
• DOI: 10.4067/S0716-09172001000300003
• Enlaces
  • Texto completo
• Resumen

  • In this note we establish a result of differentiability for the mild solution of the inhomogeneous abstract Cauchy problem when the underlying space is reflexive.

• Referencias bibliográficas
  • Citas [1] Cazenave, T. and A. Haraux, An Introduction to Semilinear Evolution Equations. Oxford University Press, Oxford, 1998.
  • [2] Eidelman, Y. S. and I. V. Tichonov, A Note on the Abstract Cauchy Problem, Semigroup Forum, 54(1997), 112-116.
  • [3] Engel, K-J. and R. Nagel, One-parameter Semigroups for Linear Evolution Equations. Springer-Verlag, New York, 2000.
  • [4] Gordon, R. A., The integrals of Lebesgue, Denjoy, Perron, and Henstock. Amer. Math. Soc., Providence, 1994.
  • [5] Henríquez, H. R. and C. Vásquez, Differentiability of Solutions of the Second Order Abstract Cauchy Problem. To appear in Semigroup Forum.
  • [6] Hewitt, E. and K. Stromberg, Real and Abstract Analysis. Springer-Verlag, Berlin, 1969.
  • [7] Hönig, C. S., The Abstract Riemann-Stieltjes Integral and its Applications to Linear Differential Equations with Generalized Boundary...
  • [8] Hönig, C. S., Semigroups and Semivariation, 14◦ Seminário Brasileiro de Análise, 1981, 185-193.
  • [9] Miyadera, I., Nonlinear Semigroups . Amer. Math. Soc, Providence, 1992.
  • [10] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York, 1983.
  • [11] Ray, W. O., Real Analysis. Prentice Hall, Englewood Cliffs, 1988.
  • [12] Travis, C. C., Differentiability of weak solutions to an abstract inhomogeneous differential equation, Proc. Amer. Math. Soc. 82 (1981),...
  • [13] Webb, G. F., Regularity of Solutions to an Abstract Inhomogeneous Linear Differential Equations. Proc. Amer. Math. Soc. 62 (1977), 271-277.
  • [14] Zaidman, S. D., Abstract Differential Equations. Research Notes in Mathematics, 36, Pitman, San Francisco, 1979.