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Title: Comparison and Stability Results for Parabolic Integro-Differential Equations
Authors: Tsai, Long-yi
Contributors: 應數系
Date: 1994
Issue Date: 2009-01-05 13:14:49 (UTC+8)
Abstract: The author considers the semilinear parabolic system (1) u˙k+Lkuk=fk(t,x,u,Hu,Ku), Bkuk=hk(t,x,u,H1u,K1u), k=1,⋯,n, where the Lk are elliptic operators in a bounded domain Ω, the Bk are Dirichlet, Neumann or mixed boundary operators, H is a linear nonlocal operator, K is a nonlocal memory operator, and H1, K1 are operators of the same type acting on the boundary of Ω. The comparison principle for a slightly more general system is given. This makes possible the use of a monotone scheme to prove existence and uniqueness for (1), provided the globally Lipschitz functions fk, gk are quasimonotone and lower and upper solutions exist. The method of vector-valued Lyapunov functions and the comparison principle yield the stability of the trivial solution to (1). Three examples demonstrate these stability results.
Relation: Proceedings Int. Math. Conf. "94 on Diffential Rquations
International Mathematics Conference '94 (Kaohsiung, 1994) (19960101), 203-217.
Data Type: conference
Appears in Collections:[應用數學系] 會議論文

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