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 \({L^{1}_{loc}(0,+ \infty; L^2(\Omega))}\) 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.
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