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I was reading Hyperbolic Partial Differential equations and its solutions through the method of characteristic. It stated that to find the solution, you need the characteristics $f$ and $g$ to intersect and at that point, you calculate the value. My question is how is it assumed that the characteristics will intersect? What if they don't?

The characteristics are $y'=f $ and $y'=g$ Can somebody help

Upstart
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  • Perhaps you could say what the PDE you are trying to solve is and how you got the equations for the characteristics from the PDE. – Deane Sep 26 '21 at 19:57
  • $a(x,y,u)u_{tt}+b(x,y,u)u_{xy}+c(x,y,u)u_{xx}=0$ – Upstart Sep 27 '21 at 06:03
  • The method of characteristics works only for first order PDE You can apply it to a second order PDE, if you can factor the differential operator into a composition of two first order operators. Also, your question is phrased a bit too vaguely. Could you provide more details on what the book says about solving a second order PDE using the method of characteristics? – Deane Sep 27 '21 at 17:54
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    I guess it also works for hyperbolic pde of second order. – Upstart Sep 27 '21 at 20:51

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