Generalized Characteristics of First-Order PDE’s

Part of the System & Control: Foundations & Applications book series (SCFA)


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.


Cauchy Problem Classical Solution Viscosity Solution Differential Game Differential Inclusion 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsRussian Academy of SciencesEkaterinburgRussia

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