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Delta shock waves for the chromatography equations as self-similar viscosity limits. (English) Zbl 1237.35114
The author studies the Riemann problem for the modified chromatography system $$ \partial_t v+\partial_x\left(\frac{v}{1+v}\right)=\partial_t w+\partial_x\left(\frac{w}{1+v}\right)=0. $$ It is shown that for special Riemann data, delta shock waves appear in the Riemann solution. The author derives the generalized Rankine-Hugoniot relation for the delta shocks. The existence and uniqueness of solutions involving delta shock waves is proved, the convergence of the self-similar vanishing viscosity approximation is also established.

35L67Shocks and singularities
35L65Conservation laws
35B30Dependence of solutions of PDE on initial and boundary data, parameters
35C06Self-similar solutions of PDE
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