Abstract
We define slow and heavy viable trajectories of differential inclusions and controlled problems. Slow trajectories minimize at each time the norm of the velocity of the state (or the control) and heavy trajectories the norm of the acceleration of the state (or the velocity of the control). Macrosystems arising in social and economic sciences or biological sciences seem to exhibit heavy trajectories.
We make explicit the differential equations providing slow and heavy trajectories when the viability domain is smooth.
Keywords
- Differential Inclusion
- Economic Science
- Contingent Cone
- Contingent Derivative
- Linear Equality Constraint
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References
Aubin, J.-P. [1981] contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions. Advances in Mathematics. Supplementary Studies. Ed. L. Nachbin. Academic Press. 160–232.
Aubin, J.-P. and A. Cellina [1984] Differential Inclusions. Springer-Verlag.
Aubin, J.-P. and I. Ekeland [1984] Applied Nonlinear Analysis. Wiley-Interscience.
Brézis, H. [1973] Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland, Amsterdam.
Cornet, B. [1981] Existence of slow solutions for a class of differential inclusions. J.Math.Anal.Appl.
Cornet, B. and G. Haddad [1983] Théorèmes de viabilité pour les inclusions différentielles du second ordre. In Haddad’s thesis, Université de Paris-Dauphine.
Haddad, G. [1981] Monotone trajectories of differential inclusions and functional differential inclusions with memory. Israel J. Math. 39, 83–100.
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© 1984 Springer-Verlag
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Aubin, JP. (1984). Slow and heavy viable trajectories of controlled problems. Smooth viability domains. In: Salinetti, G. (eds) Multifunctions and Integrands. Lecture Notes in Mathematics, vol 1091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098804
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DOI: https://doi.org/10.1007/BFb0098804
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13882-2
Online ISBN: 978-3-540-39083-1
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