caa a22 4500 606194142 CHVBK 20210128100912.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00030-015-0310-9 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0310-9 Global existence results for eikonal equation with BV initial data [Elektronische Daten] [R. Boudjerada, A. El Hajj] In this paper, we study a local and a non-local eikonal equations in one dimensional space describing the evolution of interfaces moving with non-signed velocity. For these equations, the global existence and uniqueness are available only of Lipschitz continuous viscosity solutions in some particular cases. In the present paper, we are interested in the study of the global in time existence of these equations, considering BV initial data. Based on a fundamental uniform BV estimate and the finite speed propagation property of these equations, we show, in a particular setting, global existence results of discontinuous viscosity solutions of this problem. An interesting application of these results is shown in the case of dislocation dynamics. Springer Basel, 2015 Hamilton-Jacobi equation nationallicence Non-local eikonal equation nationallicence Non-local transport equation nationallicence BV estimate nationallicence Discontinuous viscosity solution nationallicence Dislocation dynamics nationallicence Boudjerada R. AMNEDP, Faculté de Mathématiques, USTHB, El Alia, Bab Ezzouar, BP32, Algiers, Algeria aut El Hajj A. LMAC, Université de Technologie de Compiègne, 60205, Compiègne Cedex, France aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/4(2015-08-01), 947-978 1021-9722 22:4<947 2015 22 30 https://doi.org/10.1007/s00030-015-0310-9 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/s00030-015-0310-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boudjerada R. AMNEDP, Faculté de Mathématiques, USTHB, El Alia, Bab Ezzouar, BP32, Algiers, Algeria aut NATIONALLICENCE 700 1- El Hajj A. LMAC, Université de Technologie de Compiègne, 60205, Compiègne Cedex, France aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/4(2015-08-01), 947-978 1021-9722 22:4<947 2015 22 30