Abstract

We are concerned with the existence of global and blow-up solutions for the nonlinear parabolic problem described by the Hardy-Henon equation u(t) - Delta(u)(H) = |. | (gamma)(H)u(p) in H-N X (0,T), where H-N is the N-dimensional Heisenberg group, and the singular term |. | (gamma)(H) is given by the Kor & aacute;nyi norm. Our study focuses on nonnegative solutions. We establish that for gamma >= 0, the Fujita critical exponent is p(c) = 1+(2+gamma)/Q, where Q = 2N+2 is the homogeneous dimension of H-N . For -2 < gamma < 0, the solutions blow up for 1

1 + (2+gamma)+(Q+gamma). In particular, our results coincide with the results found by Georgiev and Palmieri in [17].