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Blowup in $\mathbf{L^{\infty}}$ for a class of genuinely nonlinear hyperbolic systems of conservation laws

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  • We construct a class of $3\times 3$ systems of conservation laws with all characteristic fields genuinely nonlinear, and we show the existence of entropy solutions for these that blow up in sup-norm in finite time. The solutions are constructed by considering wave patterns where infinitely many shock waves are produced in finite time. We also consider the role of entropies as a mechanism for preventing this type of singular behavior.
    Mathematics Subject Classification: 35L65, 35B05.

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