Abstract
In view of possible applications to Hamilton-Jacobi equations, to optimal control and to differential games, we extend the classical differential properties of smooth Hamiltonian and Characteristic flows to Lipschitzean ones using the contingent derivatives of their components
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35690-7_44
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Aubin, J. P. and H. Frankowska. (1990). Set Valued Analysis, Boston, Birkhäuser.
Blagodatskih, V. I. (1973). On differentiability of solutions with respect to initial conditions, Diff. Uravn., 9, 2136–2140 (in Russian).
Courant, R. (1962). Partial Differential Equations, N.Y., Interscience.
Hartman, Ph. (1964) Ordinary Differential Equations, N.Y., Wiley
Kurzweil, J. (1986) Ordinary Differential Equations, Amsterdam, Elsevier,.
Miricä, St. (1982). The contingent and the paratingent as generalized derivatives of vector-valued and set-valued mappings, Nonlinear Anal., Theory, Meth. Appl., 6, 1335–1368.
Miricâ, St. (1985). On some generalizations of the Bendixson-Picard theorem in the theory of differential equations, Bull. Math. Soc. Sci. Math. Roumanie, 29 (77), 315–328.
Miricä, St. (1987). Generalized solutions by Cauchy’s Method of Characteristics, Rend. Sem. Mat. Univ. Padova, 77, 317–350.
Miricä, St. (1995). Quasitangent differentiability with respect to initial data for Carathéodory-Lipschitz differential equations, in “Qualitative problems for Differential Equations and Control Theory”, C. Corduneanu Ed., New Jersey, Singapore, World Scientific, 81–89.
Miricâ, St. (2002). On differentiability with respect to initial data in the theory of Differential Equations, Revue Roum. Math. Pure Appl., submitted.
Miricä, St. and C. Neculäescu (1998). On a semi-smooth Hamiltonian system and related Hamilton-Jacobi equations, Anal. Univ. “Ovidius”, Constanta, Ser. Mat. 6.
Scorza-Dragoni, G. (1948). Una teorema sulla funzione continue rispètto ad una e misurabile rispètto ad un’altra variabile, Rend. Sem. Mat. Univ. Padova, X VII, 102–106.
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© 2003 IFIP International Federation for Information Processing
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Mirica, S. (2003). Differential Properties of Lipschitz, Hamiltonian and Characteristic Flows. In: Barbu, V., Lasiecka, I., Tiba, D., Varsan, C. (eds) Analysis and Optimization of Differential Systems. SEC 2002. IFIP — The International Federation for Information Processing, vol 121. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35690-7_28
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DOI: https://doi.org/10.1007/978-0-387-35690-7_28
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