I've a little troubles in proving local uniqueness of solution for Cauchy problems concerning quasilinear PDE's. It's a little bit boring, but I tried to be as clear as possible. Suppose $\Omega$ is an open and connected subset of $\mathbb{R}^2$ and let $a(x,y,z),b(x,y,z),c(x,y,z)$ scalar funct...