Abstract
In the present chapter we introduce the notion of minimax solution to first-order partial differential equation. The proposed definition is based on the weak invariance property of the graph of a generalized solution with respect to a system of differential inclusions, which will be called characteristic inclusions. This property can be given with the help of apparently different criteria, which are formulated in Sections 2 and 3. The equivalence of these criteria and the equivalence of minimax and viscosity solutions are proven in Section 4.
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© 1995 Springer Science+Business Media New York
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Subbotin, A.I. (1995). Generalized Characteristics of First-Order PDE’s. In: Generalized Solutions of First Order PDEs. System & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0847-1_1
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DOI: https://doi.org/10.1007/978-1-4612-0847-1_1
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6920-5
Online ISBN: 978-1-4612-0847-1
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