Geodesic
Smooth Dependence on Initial Data of Mild Solutions to Evolution Equations
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 3, pp. 731-754.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We prove two general theorems related to the smooth dependence on data of mild solutions to evolution Cauchy problems and provide some of their applications to the Faedo-Galerkin method for approximating solutions as well as to the existence and uniqueness of periodic solutions. 
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     title = {Smooth {Dependence} on {Initial} {Data} of {Mild} {Solutions} to {Evolution} {Equations}},
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Vidossich, Giovanni. Smooth Dependence on Initial Data of Mild Solutions to Evolution Equations. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 3, pp. 731-754. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_3_a12/

[1] R. I. Becker, Periodic solutions of semilinear equations of evolution of compact type, J. Math. Anal. Appl., 82 (1981), 33-48. | DOI | MR | Zbl

[2] A. Castro - A. C. Lazer, Results on periodic solutions of parabolic equations suggested by elliptic theory, Boll. U.M.I., 1-B (1982), 1089-1104. | MR | Zbl

[3] T. Cazenave - A. Haraux, An Introduction to Semilinear Evolution Equations, Clarendon Press, Oxford, 1998. | MR | Zbl

[4] M. W. Hirsch - C. C. Pugh, Stable manifolds for hyperbolic sets, In: "Proc. Symp. Pure Math.", vol. XIV, Amer. Math. Society (Providence, 1970), 133-163. | MR | Zbl

[5] A. Pazy, A class of semi-linear equations of evolution, Israel J. Math., 20 (1975), 23-36. | DOI | MR | Zbl

[6] J. Sotomayor, Smooth dependence of solutions of differential equations on initial data: a simple proof, Bol. Soc. Brasil. Mat., 4 (1973), 55-59. | DOI | MR | Zbl

[7] R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics (Springer-Verlag, New York, 1988). | DOI | MR | Zbl

[8] G. Vidossich, Continuous dependence for parabolic evolution equations, In: "Recent Trends in Differential Equations", R. P. Agarwal (ed.), World Scientific (Singapore, 1992), 559-568. | MR | Zbl

[9] G. Vidossich, A (semi-encyclopedic) first course in ODEs, in a "never-ending" preparation since 1974.

[10] J. R. Ward Jr., Boundary value problems for differential equations in Banach space, J. Math. Anal. Appl., 70 (1979), 589-598. | DOI | MR | Zbl