Doubly Nonlinear Diffusion Equations on Metric Graphs

Abstract

In this paper we study existence and uniqueness of solutions for a very general class of doubly nonlinear diffusion equations on metric graphs, which provide the appropriate mathematical framework to describe complex tubular networks in which axial diffusion is the main focus. Some important particular cases covered in our study are the Porous Medium Equation and the evolution equation for the $p$-Laplacian, but we also consider the case in that diffusion changes from one edge to another, which takes into account the influence of the properties of the tubules forming the network on axial diffusion. Furthermore, the problem is studied under non-homogeneous Neumann-Kirchhoff conditions on the vertices of the graph.