The Cauchy Problem for Wave Equations with NonLipschitz Coefficients

Ferruccio Colombini (1) , Guy Metivier (2)

1 Dipartimento di Matematica
2 IMB - Institut de Mathématiques de Bordeaux

In this paper we study the Cauchy problem for second order strictly hyperbolic operators when the coefficients of the principal part are not Lipschitz continuous, but only “Log-Lipschitz” with respect to all the variables. This class of equation is invariant under changes of variables and therefore suitable for a local analysis. In particular, we show local existence, local uniqueness and finite speed of propagation for the noncharacteristic Cauchy problem.

Mots clés: Wave equations; Well posedness; Cauchy problem; local existence and uniqueness; nonsmooth coefficients

Domaines: Equations aux dérivées partielles [math.AP]

Ferruccio Colombini, Guy Metivier. The Cauchy Problem for Wave Equations with NonLipschitz Coefficients. Annales Scientifiques de l'École Normale Supérieure, 2008, 41, pp 1--44. ⟨hal-00113698⟩