Hyperbolicity of First Order Quasi-Linear Equations

Abstract

The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient conditions of hyperbolicity are found in terms of the matrix of the corresponding linearized first order equations system.

Keywords

• first order differential operators
• quasi-linear equations system
• Friedrichs’ hyperbolicity
• hyperbolic matrices