Abstract :
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.
