Differentiability of solutions of the abstract cauchy problem

Authors

  • Hernán R. Henríquez Miranda Universidad de Santiago.

DOI:

https://doi.org/10.4067/S0716-09172001000300003

Keywords:

Semigroup of Operators, Abstract Cauchy Problem, Differentiability of Solutions.

Abstract

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.

Author Biography

Hernán R. Henríquez Miranda, Universidad de Santiago.

Departamento de Matemática.

References

[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.

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[7] Hönig, C. S., The Abstract Riemann-Stieltjes Integral and its Applications to Linear Differential Equations with Generalized Boundary Conditions. Notas do Instituto de Matemática e Estatística da Universidade de Sao Paulo. Série Matemática N?1, 1973.

[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), 425-430.

[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.

Published

2017-04-24

How to Cite

[1]
H. R. Henríquez Miranda, “Differentiability of solutions of the abstract cauchy problem”, Proyecciones (Antofagasta, On line), vol. 20, no. 3, pp. 295-304, Apr. 2017.

Issue

Section

Artículos