Bounded solutions of delay nonlinear evolutionary equations

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• 作者：Allaberen Ashyralyev^a ; ^b ; Deniz Agirseven^c ; ^{denizagirseven@gmail.com} ; Burcu Ceylan^d
• 关键词：35K60 ; 65M06
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：69-78
• 全文大小：396 K
• 卷排序：318

文摘

We consider the initial value problem {dudt+Au(t)=f(u(t),u(t−w)),t≥0,u(t)=φ(t),−w≤t≤0 in a Banach space EE with the positive operator AA. Theorem on the existence and uniqueness of a bounded solution of this problem is established for a nonlinear evolutionary equation with time delay. The application of the main theorem for four different nonlinear partial differential equations with time delay is shown. The first and second order of accuracy difference schemes for the solution of one dimensional nonlinear parabolic equation with time delay are presented. Numerical results are provided.