Singular shock solutions in nonlinear chromatography. (June 2018)

• Record Type: Journal Article
• Authors: Ortner, Franziska; Mazzotti, Marco
• Is Part Of: Nonlinear analysis. Volume 41(2018)
• Page Start: 66
• Page End: 81
• Publication Date: 2018-06
• Subjects: Singular shocks -- Hyperbolic partial differential equations -- Liquid chromatography; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.10.010
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a hyperbolic system of partial differential equations which is of interest in the context of nonlinear chromatography. Under certain initial and feed conditions, specified in the first part of this contribution, solutions to this system are unbounded. Characteristic properties of the singular shocks, i.e. propagation velocity and strength, are derived by two different approaches, based on Colombeau generalized functions and on box approximations of the unbounded solution, respectively. The derived expressions are found to be consistent for both approaches. Highlights: Investigation of a system of hyperbolic PDEs applied in nonlinear chromatography. Presentation of initial and feed conditions resulting in singular solutions. Derivation of properties of the singular shocks by two different approaches. Consistent results with both approaches.