Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 105 / 1 / c / Solution

WriteDifferentiating the prescribed identity $u(\psi (r,z),r,z)=0$ in its two tangential directions givesThe unit normal is $(1,-{\psi }_r,-{\psi }_z)/\sqrt{D}$, so the second item of Cauchy data becomesConsequentlySubstitution into the principal symbol from part a shows that the graph is non-characteristic exactly where

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