This paper deals with a problem of asymptotic step-like solutions of the Burgers equation with variable coefficients and a small parameter. By means of the nonlinear Wentzel–Kramers–Brillouin method, the algorithm of constructing these asymptotic solutions is proposed and statements on justification of the algorithm are proved. The obtained results are illustrated by an example, for which the first asymptotic step-like approximation is explicitly found. The asymptotic solution is global and has a form of the shock wave type function. There are also given graphs of these approximate solutions for certain numerical parameters.
Asymptotic step-like solutions of the singularly perturbed Burgers equation / Samoilenko, V.; Samoilenko, Yu.; Zappale, E.. - In: PHYSICS OF FLUIDS. - ISSN 1070-6631. - (2023). [10.1063/5.0150685]
Asymptotic step-like solutions of the singularly perturbed Burgers equation
V. Samoilenko
;E. Zappale
2023
Abstract
This paper deals with a problem of asymptotic step-like solutions of the Burgers equation with variable coefficients and a small parameter. By means of the nonlinear Wentzel–Kramers–Brillouin method, the algorithm of constructing these asymptotic solutions is proposed and statements on justification of the algorithm are proved. The obtained results are illustrated by an example, for which the first asymptotic step-like approximation is explicitly found. The asymptotic solution is global and has a form of the shock wave type function. There are also given graphs of these approximate solutions for certain numerical parameters.File | Dimensione | Formato | |
---|---|---|---|
Samoilenko_Asymptotic_2023.pdf
solo gestori archivio
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
1.32 MB
Formato
Adobe PDF
|
1.32 MB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.