JIPAM logo: Home Link
Home Editors Submissions Reviews Volumes RGMIA About Us

  Volume 7, Issue 2, Article 64
A Direct Proof of the Equivalence Between the Entropy Solutions of Conservation Laws and Viscosity Solutions of Hamilton-Jacobi Equations In One-Space Variable

    Authors: M. Aaibid, A. Sayah,  
    Keywords: Hamilton-Jacobi equation, Conservation law, Viscosity solution, Entropy solution, Front tracking method.  
    Date Received: 11/03/05  
    Date Accepted: 15/11/05  
    Subject Codes:

35L85, 49L25, 65M05.

    Editors: Ravi P. Agarwal,  

We establish a direct proof of the well known equivalence between the Crandall-Lions viscosity solution of the Hamilton-Jacobi equation $w_t+H(w_x)= 0 $ and the Kruzkov-Vol'pert entropy solution of conservation law $u_t+H(u)_x= 0 $. To reach at the purpose we work directly with defining entropy and viscosity inequalities, and using the front tracking method, and do not, as is usually done, exploit the convergence of the viscosity method.

  Download Screen PDF
  Download Print PDF
  Send this article to a friend
  Print this page

      search [advanced search] copyright 2003 terms and conditions login