“…For this reason, Xu [38] considered the case f (u) = ±|u| p or f (u) = ±|u| p−1 u, and showed the existence of global solutions and finite time blowup solutions with suitable assumptions on the initial data. The Cauchy problem of (1.6) with n ≥ 2, a = c = d = 0 was studied in [17,25,29,35], where, with small initial data, the global well-posedness and asymptotic behavior of solutions were obtained by the semigroup method, the Green function method and the energy estimate. The Cauchy problem of (1.6) in R and R n with c = d = 0 was studied in [33] and [22], respectively.…”