On Qualitative Properties of Sign-Constant Solutions of Some Quasilinear Parabolic Problems

We study the Cauchy problem for quasilinear parabolic inequalities containing squares of first derivatives an unknown function (the so-called nonlinearities KPZ type). The coefficients leading nonlinear terms considered either can be continuous functions regular case) or admit power singularities singular degree no greater than 1. For case, we prove damping global nonnegative solutions to studied. By damping, mean boundedness support a solution each positive t, uniform (with respect t) convergence zero as |x| ? ?, and vanishing (for any x) starting with certain sufficiently large t. proved that has solutions.