YIC2025

The nonlocal particle approximation of the quadratic porous medium equation

  • Iorio, Valeria (University of L'Aquila)

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In this talk, we study the approximation of the quadratic porous medium equation via nonlocal interacting particles subjet to repulsive Morse potential. We work in the set P2(R) of probability measures on R with finite second moment equipped with the 2-Wasserstein distance. We prove that the particle scheme converges towards weak solutions to the nonlocal equations as the number of particles goes to infinity. Furthermore, since the Morse potentials is rescaled to approach a Dirac delta, the scheme becomes a particle approximation for the quadratic porous medium equation. We show that in the joint limit the reconstructed density converges to a weak solution of the porous medium equation. This is a joint work with MarcoDiFrancesco(University of L’Aquila) and Markus Schmidtchen (TU Dresden).