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Global existence results for eikonal equation with BV initial data

  • R. Boudjerada
  • A. El HajjEmail author
Article

Abstract

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.

Mathematics Subject Classification

35A01 74G25 35F20 35F21 70H20 35Q74 

Keywords

Hamilton–Jacobi equation Non-local eikonal equation Non-local transport equation BV estimate Discontinuous viscosity solution Dislocation dynamics 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.AMNEDP, Faculté de MathématiquesUSTHBAlgiersAlgeria
  2. 2.LMACUniversité de Technologie de CompiègneCompiègne CedexFrance

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