Stability of Unique Solvability of Quasilinear Equations Given Additional Data

We study quasilinear equations of elliptic and parabolic type whose solutions, having bounded uniform norms or bounded uniform norms of their derivatives, are uniquely defined by the additional information about the values of these solutions on a grid. For the case in which the equations and grid values are given with an error, we present estimates of the error of approximate solutions in the uniform metric.