Abstract:

This paper deals with the global existence and blowup of solutions to a quasilinear parabolic equation ut=f(u)(Δ u+a∫Ω
u(y,t)dy-u) with nonlocal boundary condition u(x,t)=∫Ωk(x,y)u(y,t)dy on Ω, where Ω is a bounded domain in ??綆N with smooth boundary Ω. Under some hypotheses on f(s) and k(x,y), we gave sufficient conditions for the finite time blowup or global existence of solutions. In addition, the blowup rate of solutions was derived for a special case.

Key words: nonlocal boundary condition, global existence, blowup, blowup rate