A Class of Shock Wave Solution to Singularly Perturbed Nonlinear Time-Delay Evolution Equations. (24th June 2020)

• Record Type: Journal Article
• Authors: Feng, Yi-Hu; Hou, Lei
• Other Names: Rizzo Fabio Academic Editor.
• Is Part Of: Shock and vibration. Volume 2020(2020)
• Publication Date: 2020-06-24
• Subjects: Shock (Mechanics) -- Periodicals; Vibration -- Periodicals; 534.5
• DOI: 10.1155/2020/8829092
• Languages: English
• ISSNs: 1070-9622

Abstract

Abstract : 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.