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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 5-一月-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-yi zh_TW dc.date (日期) 1994 en_US dc.date.accessioned 5-一月-2009 13:14:49 (UTC+8) - dc.date.available 5-一月-2009 13:14:49 (UTC+8) - dc.date.issued (上傳時間) 5-一月-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 en en_US dc.language en-US en_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 Equations en_US dc.type (資料類型) conference en
