Existence of solutions to riemann problem for hyperbolic conservation laws containing δ-shock waves

Abstract

In this paper, we apply the limiting viscosity approach, first introduced by Dafermos [1]. to prove the existence of the solutions of Riemann problems for a class of2X2 systems of hyperbolic conservation laws containing δ-shock waves. In our analysis. Whether the system is strictly hyperbolic or not is not essential. Thus our results show that, even if the system is strictly hyperbolic, the corresponding Reimann problem does not exist in classical weak solutions for certain initial states

Keywords:

• Riemann problem
• δ-shock waves
• Critical point
• Rankine-Hugoniot conditions

AMS Subject Classification:

• 35L45
• 35L65
• 35L67

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Notes

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