The <Cauchy-Kovalevskaya theorem> says that an order-$k$ scalar <quasilinear partial differential equation> with <real analytic function>[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>
$$
u,\partial_Nu,\ldots,\partial_N^{k-1}u
$$
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.


 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-105/1/d/solution