论文标题
关于Métivier的Lax-Mizohata定理，并扩展到弱的双曲线缺陷。第一部分
On Métivier's Lax-Mizohata theorem and extensions to weak defects of hyperbolicity. Part one
论文作者
论文摘要
我们证明，对于主要差异方程的一阶完全非线性系统，在主要符号的椭圆度假设下，库奇问题在Sobolev索引指数范围内没有解决方案，这取决于初始基准的规律性。这给出了G。métivier的结果的新的，非常详细的证明[{\ IT在Cauchy问题上}，2005年]。然后，我们将此结果扩展到经历过双曲线和椭圆度过渡的系统，本着N. Lerner，Y。Morimoto和C.-J.的最新工作精神。 Xu，[{\ it cauchy-kovalevskaya解决方案的不稳定性，用于一类非线性系统}，2010年]，以及N. Lerner，T。Nguyen和B. Texier [{\ IT在一阶系统中的不稳定性的发作{{\ IT}，2018年]。
We prove that, for first-order, fully nonlinear systems of partial differential equations, under an hypothesis of ellipticity for the principal symbol, the Cauchy problem has no solution within a range of Sobolev indices depending on the regularity of the initial datum. This gives a new and greatly detailed proof of a result of G. Métivier [{\it Remarks on the Cauchy problem}, 2005]. We then extend this result to systems experiencing a transition from hyperbolicity and ellipticity, in the spirit of recent work by N. Lerner, Y. Morimoto, and C.-J. Xu, [{\it Instability of the Cauchy-Kovalevskaya solution for a class of non-linear systems}, 2010], and N. Lerner, T. Nguyen and B. Texier [{\it The onset of instability in first-order systems}, 2018].
