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Occurrence of a delta‐shock in non‐linear chromatography
Author(s) -
Mazzotti Marco
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700912
Subject(s) - constant (computer programming) , nonlinear system , mathematics , shock (circulatory) , initial value problem , riemann hypothesis , mathematical analysis , space (punctuation) , shock wave , singular solution , partial differential equation , riemann problem , simple (philosophy) , physics , mechanics , computer science , quantum mechanics , medicine , philosophy , epistemology , programming language , operating system
Abstract We consider a hyperbolic system of two first order partial differential equations that can be used to describe nonlinear chromatography, and the corresponding Riemann initial value problems. It can be shown that these equations admit classical solutions made of constant states separated by continuous (simple wave) or discontinuous (shock) transitions, but also – for exactly specified initial states – singular solutions. Such solutions are due to the occurrence of an overcompression condition that leads to the formation of a spike travelling at constant speed and increasing strength in space. Such singular solution can be observed by solving numerically a regularized form of the original equations, but eludes the application of techniques proposed in the literature to study singular shocks and delta‐shocks, which share with the system studied here its overcompressive character. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)