In this paper we study the source-type solution for the heat equation with convection: ut = △u + ■·▽un for (x,t) ∈ ST→ RN × (0,T] and u(x,0) = δ(x) for x ∈ RN, where δ(x) denotes Dirac measure in = RN,N 2,n 0 and b = (b1,...,bN) ∈ RN is a vector. It is shown that there exists a critical number pc = N+2 such that the source-type solution to the above problem exists and is unique if 0 N n < pc and there exists a unique similarity source-type solution in the case n = N+1 , while such a solution does not exist N if n > pc. Moreover, the asymptotic behavior of the solution near the origin is studied. It is shown that when 0 < n < N+1 the convection is too weak and the short time behavior of the source-type solution near the origin N is the same as that for the heat equation without convection.
