- estimates of solutions of the Cauchy problem for an anisotropic degenerate parabolic equation with double non-linearity and growing initial data

Abstract

The Cauchy problem for a degenerate parabolic equation with anisotropic -Laplacian and double non-linearity is considered. For increasing initial data local estimates for the -norm of a solution are obtained, which yield a precise characterization of the growth of solutions at infinity. An estimate for the order of the length of the time interval on which a solution is defined is found in its dependence on the initial data. Bibliography: 12 titles.