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L 1-minimization methods for Hamilton–Jacobi equations: the one-dimensional case

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Abstract

A new approximation technique based on L 1-minimization is introduced. It is proven that the approximate solution converges to the viscosity solution in the case of one-dimensional stationary Hamilton–Jacobi equation with convex Hamiltonian.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX, 77843, USA

    Jean-Luc Guermond & Bojan Popov

Authors
  1. Jean-Luc Guermond
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  2. Bojan Popov
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Correspondence to Jean-Luc Guermond.

Additional information

This material is based upon work supported by the National Science Foundation grant DMS-0510650.

J.-L. Guermond is on leave from LIMSI, UPRR 3251 CNRS, BP 133, 91403 Orsay Cedex, France.

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Guermond, JL., Popov, B. L 1-minimization methods for Hamilton–Jacobi equations: the one-dimensional case. Numer. Math. 109, 269–284 (2008). https://doi.org/10.1007/s00211-008-0142-1

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  • DOI: https://doi.org/10.1007/s00211-008-0142-1

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