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About the optimality of oscillations in non-Lipschitz coefficiebts for strictly hyperbolic equations. (English) Zbl 1170.35471

Summary: In the present paper we explain the classification of oscillations and its relation to the loss of derivatives for a homogeneous hyperbolic operator of second order. In this way we answer the open question if the assumptions to get \(C^\infty\) well posedness for weakly hyperbolic Cauchy problems or for strictly hyperbolic Cauchy problems with non-Lipschitz coefficients are optimal.

MSC:

35L15 Initial value problems for second-order hyperbolic equations
35L10 Second-order hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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References:

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