One prescribes analytic <Cauchy data>: the value of $u$ and one first derivative transverse to $\Sigma$, for example
$$
u|_\Sigma=\phi,
\qquad
\partial_\nu u|_\Sigma=\psi,
$$
where $\phi$ and $\psi$ are real analytic on $\Sigma$. Being a <non-characteristic hypersurface> allows the equation to solve for the second derivative in the transverse direction. The <Cauchy-Kovalevskaya theorem> then gives \b[one and only one local real analytic solution near $p$].

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 105 / 3 / b / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-105/3/b/ii/solution