blow-up problem for semilinear heat equation with absorption and a nonlocal boundary condition

in this paper we consider a semilinear parabolic equation u_t=δu−c(x,t)u^p for (x,t)∈ω×(0,∞) with nonlinear and nonlocal boundary condition u∣_{∂ω×(0,∞)}=∫_ωk(x,y,t)u^ldy and nonnegative initial data where p>0 and l>0. we prove some global existence results. criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given.