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

  • Sergio Segura de LeónEmail author
  • Claudete M. Webler
Article

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 L 2-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.

Mathematics Subject Classification

35K55 35K20 35K67 35D30 35K92 

Keywords

Inhomogeneous evolution equations Singular diffusion equations 1-Laplacian Dirichlet problem Total variation flow L2-initial data p-Laplacian 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Departament d’Anàlisi MatemàticaUniversitat de ValènciaBurjassotSpain
  2. 2.Departamento de MatemáticaUniversidade Estadual de MaringáMaringáBrazil

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