# American Institute of Mathematical Sciences

October  2001, 7(4): 837-853. doi: 10.3934/dcds.2001.7.837

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

 1 Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, Udine 33100, Italy 2 Mathematics Department, Indiana University, Rawles Hall, Bloomington, IN 47405, United States

Received  September 2000 Revised  February 2001 Published  July 2001

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.
Citation: Paolo Baiti, Helge Kristian Jenssen. Blowup in $\mathbf{L^{\infty}}$ for a class of genuinely nonlinear hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems, 2001, 7 (4) : 837-853. doi: 10.3934/dcds.2001.7.837
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