caa a22 4500 606194363 CHVBK 20210128100913.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0320-7 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0320-7 Global existence and uniqueness for the inhomogeneous 1-Laplace evolution equation [Elektronische Daten] [Sergio Segura de León, Claudete Webler] 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 $${L^{1}_{loc}(0,+ \infty; L^2(\Omega))}$$ L l o c 1 ( 0 , + ∞ ; L 2 ( Ω ) ) 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. Springer Basel, 2015 Inhomogeneous evolution equations nationallicence Singular diffusion equations nationallicence 1-Laplacian nationallicence Dirichlet problem nationallicence Total variation flow nationallicence L 2-initial data nationallicence p -Laplacian nationallicence Segura de León Sergio Departament d'Anàlisi Matemàtica, Universitat de València, C/Dr. Moliner 50, 46100, Burjassot, Valencia, Spain aut Webler Claudete Departamento de Matemática, Universidade Estadual de Maringá, Bloco F67, Avenida Colombo, 5790 Campus Universitário, 87020-900, Maringá, Paraná, Brazil aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1213-1246 1021-9722 22:5<1213 2015 22 30 https://doi.org/10.1007/s00030-015-0320-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0320-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Segura de León Sergio Departament d'Anàlisi Matemàtica, Universitat de València, C/Dr. Moliner 50, 46100, Burjassot, Valencia, Spain aut NATIONALLICENCE 700 1- Webler Claudete Departamento de Matemática, Universidade Estadual de Maringá, Bloco F67, Avenida Colombo, 5790 Campus Universitário, 87020-900, Maringá, Paraná, Brazil aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1213-1246 1021-9722 22:5<1213 2015 22 30