Abstract
This paper is concerned with the global solvability of the first initial boundary value problem for the quasilinear parabolic equations with two independent variables: a(t, x, u, ux)uxx - ut = f (t, x, u, ux). We investigate the case when the growth of \(\frac{{\left| {f(t,x,u,p)} \right|}}{{a(t,x,u,p)}}\) with respect to p is faster than p2 when |p| → ∞. Conditions which guarantee the global classical solvability of the problem are formulated.
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