Shock wave formation process for a multidimensional scalar conservation law

Danilov, V.; Mitrovic, D.

doi:10.1090/S0033-569X-2011-01234-9

Authors: V. G. Danilov and D. Mitrovic
Journal: Quart. Appl. Math. 69 (2011), 613-634
MSC (2000): Primary 35L65, 35L67
DOI: https://doi.org/10.1090/S0033-569X-2011-01234-9
Published electronically: June 28, 2011
MathSciNet review: 2893992
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Abstract: 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.

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