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Generalized Characteristics of First-Order PDE’s

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

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.

Keywords

Cauchy Problem Classical Solution Viscosity Solution Differential Game Differential Inclusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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