Quasilinearization for some nonlocal problems. (1993)

• Record Type: Journal Article
• Authors: Yin Yin, Yunfeng Yunfeng
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 6:Number 2(1993)
• Page Start: 117
• Page End: 122
• Publication Date: 1993
• Subjects: quasilinearization -- nonlocal problem -- semilinear parabolic equation -- upper and lower solutions -- monotone iterative technique -- quadratic convergence; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953393000115
• Languages: English
• ISSNs: 1048-9533

Abstract

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.