منابع مشابه
Well-Posedness of a Multiscale Model for Concentrated Suspensions
Abstract : In a previous work [1], three of us have studied a nonlinear parabolic equation arising in the mesoscopic modelling of concentrated suspensions of particles that are subjected to a given time-dependent shear rate. In the present work we extend the model to allow for a more physically relevant situation when the shear rate actually depends on the macroscopic velocity of the fluid, and...
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The water wave equations of ideal free–surface fluid mechanics are a fundamental model of open ocean movements with a surprisingly subtle well–posedness theory. In consequence of both theoretical and computational difficulties with the full water wave equations, various asymptotic approximations have been proposed, analysed and used in practical situations. In this essay, we establish the well–...
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where V is the average velocity of individuals, and E is the net rate of reproduction per individual at location x and time t. To complete the model, we must specify how V is related to u and E. Following [5], we assume that each individual disperses randomly with probability δ ∈ (0, 1) and disperses deterministically with an average velocity ω so as to increase his expected rate of reproductio...
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The fluid-particle interaction model introduced by the three last authors in [J. Differential Equations, 245 (2008), pp. 3503–3544] is the object of our study. This system consists of the Burgers equation with a singular source term (term that models the interaction via a drag force with a moving point particle) and of an ODE for the particle path. The notion of entropy solution for the singula...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2017
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2017.07.006