Volterra Integral Equations in Several Variables Hyperbolic Differential Equations

Abstract

The primary goal of this chapter is to present an estimation and uniqueness theory for hyperbolic differential equations in two independent variables with a completeness similar to that for ordinary differential equations in the first two chapters. If it is approached with the methods of the first chapter, this problem leads to Volterra integral equations in two variables which can be handled largely as in the one-dimensional case; even consideration of such integral equations in an arbitrary number m of independent variables produces no new difficulties. A significant part of the present chapter is devoted to the development of this theory.