Generalized Characteristics of First Order PDEs

The book explores boundary value problems for nonlinear first-order PDEs, emphasizing the method of characteristics for establishing local existence and uniqueness of solutions. It highlights the challenges posed by continuous nonsmooth functions, which can lead to nonunique solutions unless appropriate matching principles are applied. In fields like Optimal Control and Differential Games, these principles relate to cost function optimality, while in physics and mechanics, adherence to specific laws is crucial. The text also discusses the mathematical framework for generalized solutions, balancing theoretical and practical applications.