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Resolution with a constant v velocity

In this part the 2-D Burgers equation possesses only one nolinear term such as $\bar{v}$ velocity is a constant. Taking $\bar{v}$ velocity as a constant simplifies the problem and the steepening of the wave front always will be carried out in the x direction. This hypothesis avoids obtaining a curve shock wave.

\begin{displaymath}\frac{\partial u}{\partial t} + \underbrace{u \frac{\partial......tial x^{2}} +\frac{{\partial}^{2} u}{\partial y^{2}} \right)\end{displaymath}

We take $\bar{v}=0.5$ to make the comparaison between the transversal convection speed and the steepening speed of the wave front possible.

Alban Depoutre