Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities

The Cauchy problem with non-negative continuous initial function for the equation u(t) = Delta u(m) - u(p), (x, t) is an element of S =R-N x R+ is considered for 0 < p < 1, p < m. For generalized solutions of this problem with initial data increasing at infinity several results on their behaviour as t --> infinity are established. Bibliography: 11 titles.