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• W1963703804 abstract "We present in this paper several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed by a first-order partial differential equation which involves a singular source term and by an ordinary differential equation. The coupling is ensured through a drag force that can be linear or quadratic. Though this model can be considered as a simple one, its mathematical analysis is involved. We put forward a notion of entropy solution to our model, define a Riemann solver and make first steps towards well-posedness results. The main goal is to construct easy-to-implement and yet reliable numerical approximation methods; we design several finite volume schemes, which are analyzed and tested." @default.
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• W1963703804 date "2010-01-01" @default.
• W1963703804 modified "2023-10-17" @default.
• W1963703804 title "Small solids in an inviscid fluid" @default.
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• W1963703804 doi "https://doi.org/10.3934/nhm.2010.5.385" @default.
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