A system of N inelastic particles with radius 1/(2N) converges as N to infinity to weak solutions of the 1D Euler equations with unilateral density constraint and associated congestion pressure sign condition.
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Microscopic derivation of the one-dimensional constrained Euler equations
A system of N inelastic particles with radius 1/(2N) converges as N to infinity to weak solutions of the 1D Euler equations with unilateral density constraint and associated congestion pressure sign condition.