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