Shock wave formation process for a multidimensional scalar conservation law

By Vladimir G. Danilov, Darko Mitrovic. 2011

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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 character- istics 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

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics, Numerical Methods & Scientific Computing