Chapter 4 – Notes on Hyperbolic Systems of Conservation Laws and Transport Equations

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A NONLINEAR PARABOLIC-HYPERBOLIC SYSTEM FOR CONTACT INHIBITION OF CELL-GROWTH (2012, methodology): “6 in [10]) We say that a bounded velocity field b is nearly incompressible if there exists a function η ∈ L∞(RN × [0,∞)) and a positive constant C such that C η C−1 and ηt +div(ηb) = 0”
A review of the mean field limits for Vlasov equations (2014, background): “We finally refer to [3] and [50] for a more precise presentation of this subject.”
Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces (2015, background): “Uniqueness and in general the well-posedness of the Cauchy problem for advection equations like (1.4) are usually handled through the theory of renormalized solutions as introduced in [16] and improved in [1] (we refer to [2] and [15] for a very good introduction to the theory).”