  This is the first publication in which an ill-posed Cauchy problem for a
quasi- linear PDE is solved numerically by a rigorous method. More precisely,
we solve the side Cauchy problem for a 1-d quasilinear parabolc equation. The
key idea is to minimize a strictly convex cost functional with the Carleman
Weight Function in it. Previous publications about numerical solutions of
ill-posed Cauchy problems were considering only linear equations.
