The Fourier problem with nonlocal boundary conditions for a class of nonlinear parabolic equations

The paper contains theorems on the uniqueness and existence of a generalized solution to the Fourier problem (the problem without initial conditions) for a class of strongly nonlinear parabolic equations, without any restrictions on the behavior of the data and of the solution ast → ∞. A priori estimates of the solution are obtained as well. Bibliography: 8 titles. Dedicated to Olga Arsenievna Oleinik Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000.