Abstract
The present paper is concerned with the global solvability of the Cauchy problem for the quasilinear parabolic equations with two independent variables: ut=a(t,x,u,ux)uxx+f(t,x,u,ux). We investigate the case of the arbitrary order of growth of the function f(t,x,u,p) with respect to p when |p|→+∞. Conditions which guarantee the global classical solvability of the problem are given.
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