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Vanishing viscosity approach to a system of conservation laws admitting $\delta''$ waves

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  • We construct solution of Riemann problem for a system of four conservation laws admitting $\delta$, $\delta'$ and $\delta''$-waves, using vanishing viscosity method. The system considered here is an extension of a system studied in [9] and [12] and admits more singular solutions. We extend the weak formulation of [12] to the present case. For the rarefaction case, the limit is not yet fully understood, the limit given in [12] is not correct and it does not satisfy the inviscid system. In fact we show that the limit of the third component contains $\delta$ measure and the fourth component contains the measure $\delta$ and its derivative, for a special Riemann data. We also solve Riemann type initial-boundary value problem in the quarter plane.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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