A note on convergence of the solutions of Benjamin–Bona–Mahony type equations. (April 2018)

• Record Type: Journal Article
• Authors: Coclite, Giuseppe Maria; di Ruvo, Lorenzo
• Is Part Of: Nonlinear analysis. Volume 40(2018)
• Page Start: 64
• Page End: 81
• Publication Date: 2018-04
• Subjects: Singular limit -- Compensated compactness -- Benjamin–Bona–Mahony equation -- Modified Benjamin–Bona–Mahony equation -- Entropy condition; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.07.014
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider the Benjamin–Bona–Mahony and the modified Benjamin–Bona–Mahony equations, which contains nonlinear dispersive effects. We prove that as the diffusion and dispersion parameters tend to zero, the solutions of these dispersive equations converge to the entropy ones of a scalar conservation law. The argument relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L p setting.