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Hausdorff Continuous Viscosity Solutions of Hamilton-Jacobi Equations

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Large-Scale Scientific Computing (LSSC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5910))

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Abstract

A new concept of viscosity solutions, namely, the Hausdorff continuous viscosity solution for the Hamilton-Jacobi equation is defined and investigated. It is shown that the main ideas within the classical theory of continuous viscosity solutions can be extended to the wider space of Hausdorff continuous functions while also generalizing some of the existing concepts of discontinuous solutions.

The first author was partially supported by the NRF of South Africa. The second author was partially supported by the Bulgarian NSF Project DO 02-359/2008.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria,  

    R. Anguelov

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,  

    R. Anguelov & S. Markov

  3. Department of Applied Mathematics, National University of Rwanda,  

    F. Minani

Authors
  1. R. Anguelov
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  2. S. Markov
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  3. F. Minani
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads - Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Anguelov, R., Markov, S., Minani, F. (2010). Hausdorff Continuous Viscosity Solutions of Hamilton-Jacobi Equations. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_26

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  • DOI: https://doi.org/10.1007/978-3-642-12535-5_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12534-8

  • Online ISBN: 978-3-642-12535-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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