Classical solvability of a parabolic system of two nonlinear equations
D. V. Portnyagin · Differential Equations · 2011
We study the complete regularity of solutions of a nondiagonal parabolic system of quasilinear second-order differential equations in divergence form assuming that the coefficients are sufficiently slowly varying functions of their arguments and the off-diagonal terms in the coefficient matrix are sufficiently small. To this end, we use a method based on the successive approximation to the solution by smooth functions with the use of Schauder estimates at each step.