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|Title: ||Comparison and Stability Results for Parabolic Integro-Differential Equations|
|Authors: ||Tsai, Long-yi|
|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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