Nonexistence of Positive Solutions to a Semilinear Elliptic System and Blow-up Estimates for a Reaction-Diffusion SystemU

We get simple conditions under which the elliptic system yDusu p1¨ q1, yD¨ su p2¨ q2 in Rn, nG3 with piqqi)1, is1, 2 has no positive radially symmetric solutions. Then by using this nonexistence result, we establish blow-up estimates for reaction-diffusion system of Fujita type u sDuqu p1¨ q1, ¨ sD¨ qu p2¨ q2 t t with the homogeneous Dirichlet boundary value condition.