BV estimates for multicomponent chromatography with relaxation
The authors consider the system of \(2n\) balance laws \[ \begin{cases} u_t+u_x=- {1\over\varepsilon} \bigl(F(u)-v\bigr),\\ v_t= {1\over\varepsilon} \bigl(F(u)- v\bigr) \end{cases}\tag{1} \] with initial data \(u(0,x)=u_0(x)\), \(v(0,x) = v_0(x)\). This system arises from the modelling of multicomponent chromatography. Letting the relaxation parameter \(\varepsilon\to 0\), one expects that the solution to (1) converges to \[ \begin{cases} \bigl(u+F(u) \bigr)_t+ u_x=0,\\ v=F(u).\end{cases} \] The goal of the authors is to provide a rigorous proof of this convergence, valid for all solutions with small total variation. To realize this program they use in particular probabilistic arguments.
scientific article; zbMATH DE number 1492624