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Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws

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  • V. G. Danilov
  • D. Mitrovic

Abstract

We construct global smooth approximate solution to a scalar conservation law with arbitrary smooth monotonic initial data. Different kinds of singularities interactions which arise during the evolution of the initial data are described as well. In order to solve the problem, we use and further develop the weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.

Suggested Citation

  • V. G. Danilov & D. Mitrovic, 2009. "Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:350762
    DOI: 10.1155/2009/350762
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    References listed on IDEAS

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    1. V. G. Danilov, 2002. "Generalized solutions describing singularity interaction," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-14, January.
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    Cited by:

    1. S. Borazjani & P. Bedrikovetsky & R. Farajzadeh, 2014. "Exact Solution for Non‐Self‐Similar Wave‐Interaction Problem during Two‐Phase Four‐Component Flow in Porous Media," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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