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Article

Shock wave formation process for a multidimension scalar conservation law

Quarterly of Applied Mathematics. 2011. Vol. LXIX. No. 4. P. 613-634.
Danilov V., Mitrovic D.

We construct a global smooth approximate solution to a multidimensional scalar conservation law describing the shock wave formation process for initial data with small variation. In order to solve the problem, we modify the method of characteristics by introducing “new characteristics”, nonintersecting curves along which the (approximate) solution to the problem under study is constant. The procedure is based on the weak asymptotic method, a technique which appeared to be rather powerful for investigating nonlinear waves interactions.