Introduction to the Theory of Generalized Solutions of Hamilton-Jacobi Equations

The talk will focus on Hamilton-Jacobi equations, which are first-order nonlinear partial differential equations. The first part of the talk will discuss how Hamilton-Jacobi equations arise in problems of optimal control and differential games. The second part will cover the fundamentals of the theory of minimax (generalized) solutions to the Cauchy problem for Hamilton-Jacobi equations. The third part will address viscosity (generalized) solutions to such problems. For some of the results, the main ideas and key steps of the proofs will be outlined, providing a general understanding of the approaches and methods used within the discussed theory.