Interactions between discontinuities for binary mixture separation problem and hodograph method
Abstract
The Cauchy problem for firstorder PDE with the initial data which have a piecewise discontinuities localized in different spatial points is completely solved. The interactions between discontinuities arising after breakup of initial discontinuities are studied with the help of the hodograph method. The solution is constructed in analytical implicit form. To recovery the explicit form of solution we propose the transformation of the PDEs into some ODEs on the level lines (isochrones) of implicit solution. In particular, this method allows us to solve the Goursat problem with initial data on characteristics. The paper describes a specific problem for zone electrophoresis (method of the mixture separation). However, the method proposed allows to solve any system of two firstorder quasilinear PDEs for which the second order linear PDE, arising after the hodograph transformation, has the RiemannGreen function in explicit form.
 Publication:

arXiv eprints
 Pub Date:
 February 2016
 DOI:
 10.48550/arXiv.1602.01463
 arXiv:
 arXiv:1602.01463
 Bibcode:
 2016arXiv160201463E
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Numerical Analysis;
 Physics  Chemical Physics;
 35Lxx;
 35L67;
 35L40;
 35L45;
 35L50;
 35L65
 EPrint:
 19 pages, 11 figures