Existence of global Lp solutions to a system of conservation laws in chromatography with geometry effects. (August 2018)

• Record Type: Journal Article
• Authors: Liu, Shujun; Chen, Fangqi; Wang, Zejun
• Is Part Of: Nonlinear analysis. Volume 42(2018)
• Page Start: 478
• Page End: 484
• Publication Date: 2018-08
• Subjects: Conservation laws -- Chromatography system -- Lp solutions -- Viscosity method -- Compensated compactness; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.01.012
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we give the global existence of L p bounded entropy solutions for the Cauchy problem of a system of conservation laws in chromatography with geometry effects. The main difficulty lies in establishing the L p estimate of the viscosity solutions because the initial data may not be L ∞ bounded and the principle of invariant regions developed by Conley–Chuey–Smoller is invalid here. We obtain the existence of the global weak solutions using the compensated compactness method and BV estimates on viscosity solutions.