Abstract
The method of generalized quasilinearization [4] is applied to
study semilinear parabolic equation ut−Lu=f(t,x,u) with nonlocal
boundary conditions u(t,x)=∫Ωϕ(x,y)u(t,y)dy in this paper. The
convexity of f in u is relaxed by requiring f(t,x,u)+Mu2 to be convex
for some M>0. The quadratic convergence of monotone sequence is
obtained.