Differentiability of solutions of the abstract cauchy problem
DOI:
https://doi.org/10.4067/S0716-09172001000300003Keywords:
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.
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.
[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 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.
[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 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.
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