Estimates of solutions of parabolic systems in weighted Hölder classes and some of their applications

Sharp a priori estimates of weighted norms of solutions of general boundary value problems for linear parabolic systems are established in the article. These results permit one, in particular, to estimate the maxima of the moduli of derivatives of any order of solutions of homogeneous boundary value problems in terms of appropriate uniform norms of the initial data. In conjunction with homogeneous boundary value problems, inhomogeneous boundary value problems are also considered. The estimates are used to study stability questions for stationary solutions of nonlinear systems.
Bibliography: 14 titles.