On global solvability of the Caushy–Dirichlet problem for a class of nondiagonal systems with $q$-pnonlinearity, $1<q<2$

The Caushy–Dirichlet problem for a class of nondiagonal $q$-nonlinear parabolic systems is studied, $1<q<2$. In the case of two spatial variables, we constract a solution which is global in time and smooth almost everywhere. Hausdorff's dimension of the singular set is estimated.