Logarithmic Sobolev inequalities for some nonlinear PDEʹs

The aim of this paper is to study the behavior of solutions of some nonlinear partial differential equations of Mac Kean–Vlasov type. The main tools used are, on one hand, the logarithmic Sobolev inequality and its connections with the concentration of measure and the transportation inequality with quadratic cost; on the other hand, the propagation of chaos for particle systems in mean field interaction.