Quasilinearization for some nonlocal problems

[摘要] The method of generalized quasilinearization [4] is applied to study semilinear parabolic equationut−Lu=f(t,x,u)with nonlocalboundary conditionsu(t,x)=∫Ωϕ(x,y)u(t,y)dyin this paper.Theconvexity offinuis relaxed by requiringf(t,x,u)+Mu2to be convex for someM>0. The quadratic convergence of monotone sequence is obtained.

[学科分类] 应用数学