Doubly Nonlinear Diffusive PDEs: New Existence Results via Generalized Wasserstein Gradient Flows

Source abstract

Abstract. We prove an existence result for a large class of PDEs with a nonlinear Wasserstein gradient flow structure. We use the classical theory of Wasserstein gradient flow to derive an Energy Dissipation Inequality (EDI) formulation of our PDE and prove that under some integrability assumptions on the initial condition the PDE is satisfied in the sense of distributions.