Abstract
In this paper, we consider the initial value problem for a \(2 \times 2\) system of non-strictly hyperbolic conservation laws. The first equation is a convex conservation law whose flux has linear growth at infinity and has an asymptotic limit under a scaling. The second equation is linear and exhibits measure-valued solution even if the initial data is smooth with compact support. We use a scaling argument to derive explicit formula of solution for the system with the asymptotic flux function where the second equation becomes linear with discontinuous coefficient. We also study properties of solution when the initial data is periodic with zero mean over the period. Our theory is illustrated using the Lax equation.
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Acknowledgements
The authors are thankful to the referee for constructive suggestions which improved the presentation of the paper.
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The first author was supported by the TIFR CAM Doctoral Fellowship and the second author was supported by the Raja Ramanna Fellowship.
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Das, A., Joseph, K.T. Explicit Solution of a Non-strictly Hyperbolic System with Discontinuous Flux Using a Scaling Argument. Differ Equ Dyn Syst (2022). https://doi.org/10.1007/s12591-022-00620-z
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DOI: https://doi.org/10.1007/s12591-022-00620-z