The Cauchy-Kovalevsky Theorem

The Cauchy-Kovalevsky Theorem states that we can solve a k-th order quasilinear partial differential equation with analytic Cauchy data specified on an analytic non-characteristic hypersurface. We will present the proof of this theorem, following the exposition in Section 4.6 of Evans's Partial Differential Equations. Time-permitting, we will discuss the role of this theorem in the proof of the Cartan-Janet local embedding theorem.