Convergence Results for Some Conservation Laws with a Reflux Boundary Condition and a Relaxation Term Arising in Chemical Engineering
- 1 September 1998
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 29 (5) , 1200-1223
- https://doi.org/10.1137/s003614109630793x
Abstract
This paper deals with a system of 2N semilinear transport equations with a boundary condition of imposed flux. The right-hand side models some kinetic exchange between two phases. It is thus a stiff term involving a small parameter which will tend to 0. Using compensated compactness, one proves, under some assumptions on the flux, that the solution to this system converges to a solution to a system of N quasilinear equations, a solution which satisfies a set of entropy inequalities. Thus the reflux boundary condition for the quasi-linear system is given a meaning.Keywords
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