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https://nccur.lib.nccu.edu.tw/handle/140.119/21808
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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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