Solvability of nonlinear heat equation in class of unbounded functions with degeneration of coefficient near derivative with respect to time

In this paper, we consider quasilinear parabolic equations which degenerate on a solution due to a multiplier of the derivative with respect to time. In the many-dimensional case, we prove the existence of a solution of a general boundary-value problem from a class of unbounded functions. Restrictions to nonlinearity of the multiplier of the derivative with respect to time are different from ones considered before by other authors.