ABSTRACT
One can study hyperbolic equations either as second-order partial differential equations or as equivalent systems of two first-order equations. Because of the exceptional difficulties encountered for this class of equations, in this chapter we will consider both approaches. For simplicity, let us consider first the wave equation () u xx − u yy = 0. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429493393/adca3d7b-dc1b-488c-907a-7abe95228779/content/eq1774.tif"/> In (8.1), the variable y, again, represents time. However, the literature is sufficiently divided between the use of (8.1) and u xx − u tt = 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429493393/adca3d7b-dc1b-488c-907a-7abe95228779/content/eq1775.tif"/> that we will continue this time to use (8.1).
