In this chapter we present basic concepts and results for hyperbolic equations. We begin in Sect. 11.1 with a short discussion of characteristic directions, curves, and surfaces. In Sect. 11.2 we study the model wave equation. We use the method of eigenfunction expansions to solve the standard initial boundary value problem, and apply the energy method to study uniqueness and domains of dependence. In Sect. 11.3 we reduce the solution of first order scalar first order partial differential equations to integration along characteristic curves, and in Sect. 11.4 we extend this approach to symmetric first order system, and consider finally symmetric hyperbolic systems in more than one space variable by energy arguments.
KeywordsWave Equation Characteristic Polynomial Hyperbolic Equation Energy Method Characteristic Direction
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