Modulus of continuity of the coefficients and (non)quasianalytic solutions in the strictly hyperbolic Cauchy problem
Modulus of continuity of the coefficients and (non)quasianalytic solutions in the strictly hyperbolic Cauchy problem
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严格双曲柯西问题中系数的连续模和（非）准解析解
DOI：
10.1016/j.jmaa.2006.12.019
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
F. Colombini
中科院分区：
文献类型：
--
作者：
M. Cicognani;F. Colombini
在严格双曲柯西问题中，我们研究了超可微函数和泛函的Beurling-Roumieu类中系数随时间变化的连续模与适定性之间的关系.我们在非拟解析类中发现了适定性，假设系数具有连续模tω（1/t）使得ω 01ω（1/t）dt<+∞.这个条件很尖锐，因为在∫01ω（1/t）dt=+∞的情况下，我们提供了仅在准分析类中适定的柯西问题的例子。
In the strictly hyperbolic Cauchy problem, we investigate the relation between the modulus of continuity in the time variable of the coefficients and the well-posedness in Beurling–Roumieu classes of ultradifferentiable functions and functionals. We find well-posedness in nonquasianalytic classes assuming that the coefficients have modulus of continuity tω(1/t) such that ∫01ω(1/t)dt<+∞. This condition is sharp because, in the case ∫01ω(1/t)dt=+∞, we provide examples of Cauchy problems which are well-posed only in quasianalytic classes.