Bounded solutions of delay nonlinear evolutionary equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:318

Article

Ashyralyev, Allaberen^1,2  Agirseven, Deniz³  Ceylan, Burcu⁴ 

[1] Near East Univ, Dept Math, Nicosia 10, Cyprus

[2] Inst Math & Math Modeling, Alma Ata 050010, Kazakhstan

[3] Trakya Univ, Dept Math, Edirne, Turkey

[4] Trakya Univ, Dept Computat Sci, Edirne, Turkey

关键词: Delay evolutionary equations;    Bounded solution;    Difference schemes;    Existence and uniqueness;    Positive operator;    Banach space;   

DOI  :  10.1016/j.cam.2016.11.046

来源: Elsevier

【 摘 要 】

We consider the initial value problem {du/dt + Au(t) = f (u(t), u(t w)), t >= 0, u(t) = phi(t), -w <= t <= 0 in a Banach space E with the positive operator A. 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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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