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Relative Entropy Method for Particle Approximation of the Landau Equation for Maxwellian Molecules
José Antonio Carrillo, Xuanrui Feng, Shuchen Guo +2
We derive the spatially homogeneous Landau equation for Maxwellian molecules from a natural stochastic interacting particle system. More precisely, we control the relative entropy…
Mean-field derivation of Landau-like equations
José Antonio Carrillo, Shuchen Guo, Pierre-Emmanuel Jabin
We derive a class of space homogeneous Landau-like equations from stochastic interacting particles. Through the use of relative entropy, we obtain quantitative bounds on the distan…
Interacting particle approximation of cross-diffusion systems
Jose Antonio Carrillo, Shuchen Guo
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the no…
Novel approaches for the reliable and efficient numerical evaluation of Landau-type operators
Jose Antonio Carrillo, Mechthild Thalhammer
Numerical approximations of Landau-type operators represent fundamental components of time integration methods for demanding problems such as inhomogeneous Vlasov-Landau-type equat…