Linearization of completely exceptional second order hyperbolic conservative equations

Abstract

The formation of nonlinear shocks does not occur for nonlinear hyperbolic partial differential equations which are “completely exceptional”. In some sense the solutions of these equations exhibit a behaviour similar to that of linear equations. We present a procedure which allows to transform, under suitable conditions, such type of equations to linear canonical form. The procedure is valid for more than one space dimension and allows also to characterize classes of linearizable systems.

Keywords:

• conservative hyperbolic equations
• complete exceptionally
• Monge-Ampère equation
• Lie groups

Additional information

Notes on contributors

Andrea Donato