## Journées équations aux dérivées partielles

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Mark Williams
Turning points at infinity and stability of detonations
Journées équations aux dérivées partielles (2015), Exp. No. 12, 8 p., doi: 10.5802/jedp.641
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Résumé - Abstract

We begin by looking at a few simple examples of turning points in systems of ODEs depending on parameters, and then focus on the difficult case where the turning point occurs at infinity. We explain how turning points at infinity arise in a problem of detonation stability that was studied by J. J. Erpenbeck in the 1960s. In this problem the relevant system of ODEs describes the evolution of high frequency perturbations of a detonation profile, and the parameters on which the system depends are the perturbation frequencies. The resolution of the problem requires an analysis of the turning point at infinity that is uniform with respect to the parameters. This is joint work with Olivier Lafitte and Kevin Zumbrun.

Bibliographie

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