Synopses & Reviews
This text presents an approach to partial differential equations that can be considered as a non-classical method of characteristics, according to which the generalized solution (the minimax solution) is assumed to be flow invariant with respect to the so-called characteristic inclusions. The research on minimax solutions employs methods of the theory of differential games, dynamical optimization and nonsmooth analysis. At the same time, this research has contributed to the development of these new branches of mathematics. The book is intended as a self-contained exposition of the theory of minimax solutions. It includes existence and uniqueness results, examples of modelling and applications to the theory of control and differential games.
Review
"Subbotin's book is a very valuable addition to the literature." -- Mathematical Reviews "The book is printed excellently and clearly. The explanations concerning the content are distinguished of high correctness and equipped with numerous examples and illustrations." -- ZAA
Synopsis
In this book, the authors present another approach that can be considered as a non-classical method of characteristics, according to which the generalized solution ( called the minimax solution ) is assumed to be weak invariant with respect to the so-called characteristic inclusions.