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A simple 1D model of inviscid fluid-solid interaction. (English) Zbl 1151.76033
Summary: We analyze a one-dimensional fluid-particle interaction model, composed by the Burgers equation for fluid velocity and an ordinary differential equation which governs the particle motion. The coupling is achieved through a friction term. One of the novelties is to consider entropy weak solutions involving shock waves. The difficulty is the interaction between these shock waves and the particle. We prove that the Riemann problem with arbitrary data always admits a solution, which is explicitly constructed. Besides, two asymptotic behaviors are described: the long-time behavior and the behavior for large friction coefficients.

MSC:
76T15 Dusty-gas two-phase flows
76L05 Shock waves and blast waves in fluid mechanics
35Q35 PDEs in connection with fluid mechanics
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