Variational principle for general diffusion problems
The authors study the existence of weak solutions for a class of nonhomogeneous parabolic equations of Fokker-Plank type having time dependent nonlinear diffusion term and drift coefficient, and with Neumann type boundary conditions. The weak solutions are constructed (approximated) by using a variational principle expressed in terms of the Wasserstein distance. A needed maximum principle for the equations under consideration is previously established.
scientific article; zbMATH DE number 2135338