Geometric-Qualitative Approach

Abstract

In this chapter, following a geometric-qualitative approach to partial differential equations, we will consider important methods and concepts concerning quasilinear and nonlinear PDEs (in two independent variables) and solutions of classical and generalized Cauchy problems (with continuous and discontinuous initial data), namely, the Lagrange method of characteristics and its generalizations, the concepts of solution surfaces (or integral surfaces), general solutions, discontinuous or weak solutions, solution profiles at infinity, complete integrals, the Monge cone, characteristic directions.