If I am using the method of characteristics to solve a PDE [tex]\Psi(x,t)[/tex] (first order, semi-linear), and after using the method of characteristics I find that the Jacobian(adsbygoogle = window.adsbygoogle || []).push({});

[tex]|\frac{\partial{(x,t)}}{\partial{(\sigma,\eta)}}| = 0[/tex]

(where [tex]\sigma[/tex] and [tex]\eta[/tex] are parameters for the curve) does this imply that no solution exists, or just that the solution is not unique? I could not find this in my textbook.

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# Characteristic method + Jacobian

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