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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,  
 
  Abstract:

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. ;


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