Quasilinearization for some nonlocal problems. (1993) - Yin Yin, Yunfeng Yunfeng
Abstract : The method of generalized quasilinearization [4] is applied to study semilinear parabolic equation u t − L u = f ( t, x, u ) with nonlocal boundary conditions u ( t, x ) = ∫ Ω ϕ ( x, y ) u ( t, y ) d y in this paper. The convexity of f in u is relaxed by requiring f ( t, x, u ) + M u 2 to be convex for some M > 0 . The quadratic convergence of monotone sequence is obtained.