On existence and uniqueness theorems of regular week solutions for the first boundary-value problem for quasilinear degenerated parabolic second-order equations

We consider the first boundary-value problem for quasilinear degenerated $(A, \vec b)$-parabolic equations of divergent form in $Q=\Omega\times(T_1, T_2)$ where $\Omega$ is a bounded domain in $\mathbb R^n$, $n\geqslant1$. Existenceand uniqueness theorems of regular weak solutions for these equations are established.