Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the scalar diffusive dispersive conservation laws. (December 2019)

• Record Type: Journal Article
• Authors: Yoshida, Natsumi
• Is Part Of: Nonlinear analysis. Volume 189(2019)
• Publication Date: 2019-12
• Subjects: 35K55 -- 35B40 -- 35L65; Korteweg–de Vries–Burgers–Kuramoto equation -- asymptotic behavior -- rarefaction wave; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111573
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar diffusive dispersive conservation laws where the far field states are prescribed. Especially, we deal with the generalized models for Korteweg–de Vries–Burgers–Kuramoto equation. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity.