Long time behavior of solutions to semilinear parabolic equations with nonlo-
cal nonlinear source ut − u = R
g(u)dx in
× (0, T) and with nonlocal boundary con-
dition u(x, t) = R
f(x, y)u(y, t)dy on @
× (0, T) is studied. The authors establish local
existence, global existence and nonexistence of solutions and discuss the blowup properties
of solutions. Moveover, they derive the uniform blowup estimates for g(s) = sp(p > 1) and
g(s) = es under the assumption R
f(x, y)dy < 1 for x 2 @
.