Equacions de difusió no lineal i cinètiques; comportament asintòtic i aproximació numèrica

The main objective of this project is to improve the knowledge on analytical and numerical aspects of some nonlinear Partial Differential Equations (PDEs) arising in either kinetic models of stastical mechanics, their asymptotic limits and approximations or nonlinear diffusion models. These equations include nonlinear kinetic and diffusion PDEs with applications in charge-particle transport, cellulat movement, granular gases, From ana analytical point of view, we shall study the dynamical and asymptotic behavior in different regimes and their relations to optimal mass transport theory and relative entropy tecniques. From a numerical point of view, we sill sevvelop numerical methods adapted to purely transport kinetic equations, their optimal numercial implementation and applications to modeling and simyulation of semiconductors and plasmas