Global blow-up for a localized nonlinear parabolic equation with a nonlocal boundary condition

This paper deals with the blow-up properties of positive solutions to a nonlinear parabolic equation with a localized reaction source and a nonlocal boundary condition. Under certain conditions, the blowup criteria is established. Furthermore, when f ( u ) = u p , 0 < p ⩽ 1 , the global blowup behavior is shown, and the blowup rate estimates are also obtained.