The limits of Riemann solutions to the simplified pressureless Euler system with flux approximation. (3rd May 2018)

• Record Type: Journal Article
• Authors: Sun, Meina
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 12(2018)
• Page Start: 4528
• Page End: 4548
• Publication Date: 2018-05-03
• Subjects: delta shock wave -- linear flux approximation -- pressureless Euler system -- Riemann problem -- vacuum state; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4912
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The formation of vacuum state and delta shock wave in the solutions to the Riemann problem for the simplified pressureless Euler system is considered under the linear approximations of flux functions. The method is to perturb the non‐strictly hyperbolic system into a nearby strictly hyperbolic system by introducing appropriately the linear approximations of flux functions. The solutions to the Riemann problem for the approximated system can be constructed explicitly and then the formation of vacuum state and delta shock wave can be observed by taking the perturbation parameter tend to zero in the solutions.