A Remark on the Global Solvability of the Cauchy Problem for Quasilinear Parabolic Equations

The present paper is concerned with the global solvability of the Cauchy problem for the quasilinear parabolic equations with two independent variables: ut aŽt, x, u,ux.ux x fŽt, x, u, ux.. We investigate the case of the arbitrary order of growth of the function fŽt, x, u, p.with respect to p when p . Conditions which guarantee the global classical solvability of the problem are given.