Prove the converse of Theorem 1. That is, prove that a
Chapter 9, Problem 2(choose chapter or problem)
Prove the converse of Theorem 1. That is, prove that a level surface of t(x) is characteristic if (x) satises the nonlinear PDE |(x)| 1 c . () (Hint: Differentiate the equation () to getij(x)j(x)=0, where subscripts denote partial derivatives. Show that a curve, which satises the ODE dx/dt =c2(x), also satises d2x/dt2 =0 and hence is a ray. Show that t (x) is constant along a ray. Deduce that any level surface of t (x) is characteristic.)
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