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Article Dans Une Revue American Journal of Mathematics Année : 2010

INSTABILITY OF THE CAUCHY-KOVALEVSKAYA SOLUTION FOR A CLASS OF NONLINEAR SYSTEMS

Résumé

We prove that in any C∞-neighborhood of an analytic Cauchy datum, there exists a smooth function such that the corresponding initial value problem does not have any classical solution for a class of first-order nonlinear systems. We use a method initiated by G. M´etivier for elliptic systems based on the representation of solutions and on the FBI transform; in our case the system can be hyperbolic at initial time, but the characteristic roots leave the real line at positive times.
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Dates et versions

hal-01116733 , version 1 (14-02-2015)

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  • HAL Id : hal-01116733 , version 1

Citer

Nicolas Lerner, Yoshinori Morimoto, Chao-Jiang Xu. INSTABILITY OF THE CAUCHY-KOVALEVSKAYA SOLUTION FOR A CLASS OF NONLINEAR SYSTEMS. American Journal of Mathematics, 2010, 132, pp.99-123. ⟨hal-01116733⟩
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