The present paper concerns a Riemann problem for a conservation law with a nonlinear flux involving a step function. In a convenient space of distributions, we will see the emergence of a delta standing wave which extends the corresponding result, obtained by Sun in 2013 and also by Shen in 2014, for a linear flux. In the nonlinear setting, a new phenomenon arises: starting from a vanishing initial condition, the concentration of matter in a fixed point becomes possible. These results are easy to get essentially because, in our approach, the product of distributions is a distribution that does not depend of approximation processes.
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Research Article| July 12 2019
A nonlinear conservation law with a step function involving the flux: A distributional approach
C. O. R. Sarrico; A nonlinear conservation law with a step function involving the flux: A distributional approach. J. Math. Phys. 1 July 2019; 60 (7): 071504. https://doi.org/10.1063/1.5086161
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