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An Introduction to Partial Differential Equations by Jacob Rubinstein, Yehuda Pinchover

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2

First-order equations

2.1 Introduction

A first-order PDE for an unknown function u (x1, x2, . . ., xn) has the following general form:

image

(2.1)

where F is a given function of 2n + 1 variables. First-order equations appear in a variety of physical and engineering processes, such as the transport of material in a fluid flow and propagation of wavefronts in optics. Nevertheless they appear less frequently than second-order equations. For simplicity we shall limit the presentation in this chapter to functions in two variables. The reason for this is not just to simplify the algebra. As we shall soon observe, the solution method is based on ...

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