One-dimensional nonlinear chromatography system and delta-shock waves (Q378075)

The author considers the Riemann problem for the following nonlinear chromatography system \[ \partial_t u+\partial_x\bigl(u/(1-u+v)\bigr)= \partial_t v+\partial_x\bigl(v/(1-u+v)\bigr)=0 \] and proves existence of a weak solution, which may contain delta-shock waves in the both components \(u,v\). The global solutions are also constructed for the generalized Riemann problem when the initial data contains an intermediate constant state. The asymptotic behavior of these solutions as \(t\to\infty\) is analyzed. It is also shown that solutions of the generalized Riemann problem converge to the Riemann solution as the length \(\varepsilon\) of intermediate segment tends to zero.