Global existence and uniqueness for the inhomogeneous 1-Laplace evolution equation

Abstract

In this paper we introduce a new approach to the Dirichlet problem for the total variation flow in a bounded domain and analyze the associated inhomogeneous problem. We prove global existence and uniqueness for source data belonging to (Formula Presented.) and L2-initial data. We compare solutions corresponding to different data as well as study the long-term behaviour of the solutions. We also show explicit examples of radial solutions.