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In this paper,we investigate a reaction-diffusion equation ut-duxx =au + ∫t0up(x,τ)dT+k(x) with double free boundaries.We study blowup phenomena in finite time and asymptotic behavior of time-global solutions.Our results show if ∫h0-hok(x)φ1dx is large enough,then the blowup occurs.Meanwhile we also prove when T* ＜ +oo,the solution must blow up in finite time.On the other hand,we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently.