A Class of Shock Wave Solution to Singularly Perturbed Nonlinear Time-Delay Evolution Equations
Joint Authors
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-06-24
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Nonlinear singularly perturbed problem for time-delay evolution equation with two parameters is studied.
Using the variables of the multiple scales method, homogeneous equilibrium method, and approximation expansion method from the singularly perturbed theories, the structure of the solution to the time-delay problem with two small parameters is discussed.
Under suitable conditions, first, the outer solution to the time-delay initial boundary value problem is given.
Second, the multiple scales variables are introduced to obtain the shock wave solution and boundary layer corrective terms for the solution.
Then, the stretched variable is applied to get the initial layer correction terms.
Finally, using the singularly perturbed theory and the fixed point theorem from functional analysis, the uniform validity of asymptotic expansion solution to the problem is proved.
In addition, the proposed method possesses the advantages of being very convenient to use.
American Psychological Association (APA)
Feng, Yi-Hu& Hou, Lei. 2020. A Class of Shock Wave Solution to Singularly Perturbed Nonlinear Time-Delay Evolution Equations. Shock and Vibration،Vol. 2020, no. 2020, pp.1-8.
https://search.emarefa.net/detail/BIM-1212751
Modern Language Association (MLA)
Feng, Yi-Hu& Hou, Lei. A Class of Shock Wave Solution to Singularly Perturbed Nonlinear Time-Delay Evolution Equations. Shock and Vibration No. 2020 (2020), pp.1-8.
https://search.emarefa.net/detail/BIM-1212751
American Medical Association (AMA)
Feng, Yi-Hu& Hou, Lei. A Class of Shock Wave Solution to Singularly Perturbed Nonlinear Time-Delay Evolution Equations. Shock and Vibration. 2020. Vol. 2020, no. 2020, pp.1-8.
https://search.emarefa.net/detail/BIM-1212751
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1212751