The Riemann problem for pressureless compressible fluid system with time- and space-dependent external force

Abstract

We concern with Riemann problem for an one-dimensional pressureless compressible fluid system with time- and space-dependent external force. Under the concept of α-solution to this model, we obtain the α-solutions to the Riemann problem and the criteria of appearance of each α-solution. It is observed that the expressions of these α-solutions do not depend on α. Besides, the vacuum solution arises although the initial values do not involve vacuum. Furthermore, the delta wave solution emerges for certain initial values, in which internal energy variable and density variable contain the Dirac measure. Finally, our technique can be applied to study the other singular solutions to systems of conservation laws with a source term.

Keywords

• Compressible fluids
• Riemann problem
• α-solution
• Delta wave
• Vacuum state