On differentiability of solutions to the nonlinear transport equation in bounded Radon measures

We consider the nonlinear transport equation in the space of bounded Radon measures. Amongst its applications are structure population model or crowd dynamics. Previous results concerning this type of equations do not allow us to get the differentiability of solutions with respect to a perturbation of the system. We have found a new setting, which allows stating such regularity. In this setting, the parameters of the equation are C^{1+\alpha} and then the derivative of the solution is an element of the space predual to (C^{1+\alpha}).

During the talk, I would like to give a sketch of the proof. These results are based on a joint project with Piotr Gwiazda and Sander C. Hille.