Nonlinear PDE. Singularities, Propagation, Applications

Abstract

This text deals with the singularities of the solutions of several classes of nonlinear partial differential equations and systems. Applications of the results here obtained are given for the Monge-Ampère equation, for quasi-linear systems arising in fluid mechanics, and for some nonlinear integrodifferential equations useful in solid body mechanics in media with memory. In our investigations we have used two different approaches - the classical method of characteristics in the case of systems with one space variable and the machinery of paradifferential operators in the multi­dimensional case.