Secondary critical exponent and life span for a doubly singular parabolic equation with a weighted source

This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div(|∇u|p−2∇um)+α|x|uq, (x,t)∈ℝN×(0,T),where N ≤ 1, 1 < p < 2, satisfying 2 < p + m < 3, q > 1, and α > N(3 – p – m) – p. We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem. Moreover, the life span of solutions is also studied.