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

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- Solution d

Solution

The Cauchy-Kovalevskaya theorem says that an order-

k

scalar quasilinear partial differential equation with real-analytic coefficients has a unique local real-analytic solution near each point of a real-analytic non-characteristic hypersurface, provided the prescribed Cauchy data

u, \partial_{N} u, \dots, \partial_{N}^{k - 1} u

are real analytic there. The uniqueness is among local real-analytic solutions agreeing with all of those data.

Solved by gpt-5.6-sol high.

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