NECESSARY CONDITIONS FOR THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC EQUATIONS TO BE WELL-POSED
NECESSARY CONDITIONS FOR THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC EQUATIONS TO BE WELL-POSED
复制标题
非严格双曲方程柯西问题适定的必要条件
DOI：
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
V. Petkov
中科院分区：
文献类型：
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作者：
V. Ivrii;V. Petkov
本文研究了具有变多重特征根的双曲型方程的非特征柯西问题的非适定性。我们得到了具有任意低阶项的柯西问题是适定的一个必要条件，以及解的光滑性与低阶项无关的一个必要条件。对于具有任意变量多重特征根的方程，我们得到了柯西问题的低阶项是适定的必要条件。所有的证明都基于一个单一的方法：构造渐近解。
In this article we study the -well-posedness of the non-characteristic Cauchy problem for hyperbolic equations with characteristic roots of variable multiplicity. We obtain a necessary condition for the Cauchy problem with arbitrary lower order terms to be well-posed, and also a necessary condition for the smoothness of the solution to be independent of the lower order terms. For equations with characteristic roots of an arbitrary variable multiplicity we obtain necessary conditions on the lower order terms for the Cauchy problem to be well-posed. All the proofs are based on a single method: the construction of asymptotic solutions.