N Wave and Periodic Wave Solutions for Burgers Equations

This article concerns the initial boundary value problem for the non linear dissipative Burgers equation. Our general purpose is to describe the asymptotic behavior of the solution in the Cauchy problem with a small parameter ε for this equation and to discuss in particular the cases of the N wave shock and periodic wave shock. we show that the solution of Cauchy problem of viscid equation approach the shock type solution for the Cauchy problem of the inviscid equation for each case. The results are formulated in classical mathematics and proved with infinitesimal techniques of Non Standard Analysis.