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題名 Comparison and Stability Results for Parabolic Integro-Differential Equations
作者 Tsai, Long-yi
貢獻者 應數系
日期 1994
上傳時間 5-Jan-2009 13:14:49 (UTC+8)
摘要 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.
關聯 Proceedings Int. Math. Conf. "94 on Diffential Rquations
     International Mathematics Conference `94 (Kaohsiung, 1994) (19960101), 203-217.
資料類型 conference
dc.contributor 應數系en_US
dc.creator (作者) Tsai, Long-yizh_TW
dc.date (日期) 1994en_US
dc.date.accessioned 5-Jan-2009 13:14:49 (UTC+8)-
dc.date.available 5-Jan-2009 13:14:49 (UTC+8)-
dc.date.issued (上傳時間) 5-Jan-2009 13:14:49 (UTC+8)-
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/21808-
dc.description.abstract (摘要) 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.-
dc.format application/en_US
dc.language enen_US
dc.language en-USen_US
dc.language.iso en_US-
dc.relation (關聯) Proceedings Int. Math. Conf. "94 on Diffential Rquations
     International Mathematics Conference `94 (Kaohsiung, 1994) (19960101), 203-217.		en_US
dc.title (題名) Comparison and Stability Results for Parabolic Integro-Differential Equationsen_US
dc.type (資料類型) conferenceen