We are concerned with the study of the following nonlocal diffusion problem,
ut = J * u − u + f(u) in W× (0, T),
u = 0 in (RN-W ) × (0, T),
u(x, 0) = u0(x)³ 0 in , W
where W is a bounded domain in RN with smooth boundary ¶W, J*u(x, t) = ¦RN J(x - y)u(y, t)dy, J: RN ® R is a kernel which is nonnegative, symmetric (J(z) = J(-z)), bounded and = 1 and f : (-¥, b) ® (0, ¥) is a C1 convex, increasing function, lims a®b ¦ (s) = ¥, ¦b0 d/¦(a)< ¥ with b a positive constant. The initial datum u0Î = C1 o/(W) is nonnegative in W, with ‖u0‖¥ =supzÎW ïU0(x)ïnder some assumptions, we show that if ku0k1 is large enough, then the solution of the above problem quenches in a finite time, and its quenching time goes to that of the solution of the differential equation, a’ (t) = ¦ (a (t)), t > 0, a (0) = ‖u0‖¥, as ‖u0‖¥ tends to b. Finally, we give some numerical results to illustrate our analysis.