RASCLE , Michel

We consider the one-dimensional Euler-Poisson system in the isothermal case, with a friction coefficient $ {\varepsilon ^{ - 1}}$. When $ \varepsilon \to {0_ + }$, we show that the sequence of entropy-admissible weak solutions constructed in [PRV] converges to the solution to the drift-diffusion equations. We use the scaling introduced in...

We consider the system of isothermal Euler Equations with a strong damping. For large BV solutions, we show that the density converges to the solution to the heat equation when the friction coefficient $ε^{−1}$ tends to infinity. Our estimates are already valid for small time, including in the initial layer. They are global in space (and even...

Nonlinear geometric optics with various frequencies for entropy solutions only in $L^∞$ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and $L^1$-stability. New multidimensional features are...

We discuss the modelling of interacting populations through pursuit-evasion ---- or attraction-repulsion ---- principles~: preys try to escape chasers, chasers are attracted by the presence of preys. We construct a hierarchy of models, ranging from ODEs systems with finite numbers of individuals of each population, to hydrodynamic systems....

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