ABSTRACT

This is the first family of global solutions of (2), that we consider. Namely, in the range (3), we consider the standard global self-similar solutions defined for all t > 0:

uS(x, t) = t − 1p−1 f(y), y = x√

t , (8)

where f solves a semilinear elliptic equation of the form { A(f) ≡ Δf + 12 y · ∇f + 1p−1 f + |f |p−1f = 0 in IRN , f(y) has exponential decay at infinity.