Applications of the differential calculus to nonlinear parabolic operators

Abstract

We consider the Cauchy-Dirichlet problem for second order quasilinear non-divergence form parabolic equations with discontinuous data in a bounded cylinder. Supposing existence of strong solution and applying the Implicit Function Theorem we show that for any small essentialy bounded perturbations of the data there exists, locally in time, exactly one solution close to the fixed one which depends smoothly on the data. Moreover, applying the Newton Iteration Procedure we obtain an approximating sequence for the fixed solution