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The Riemann problem with delta initial data for pressureless compressible Euler equations with a constant external force. (Chinese. English summary) Zbl 1438.35273

Summary: The Riemann problem with delta initial data for pressureless compressible Euler equations with a constant external force is considered. We first study the corresponding perturbed initial value problem. Then, under the stability theory of weak solutions to one-dimensional nonlinear systems of conservation laws, six kinds of exact solutions are obtained by analyzing the limits of solutions to the corresponding perturbed initial value problem. In particular, for certain initial data, a delta contact discontinuity with Dirac delta function in both density and internal energy arises in the solutions, which is an important nonlinear phenomenon. Besides, the results show clearly the influence of the constant external force on the structures of solutions.

MSC:

35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35Q31 Euler equations
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