On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients
On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients
复制标题
系数正则性影响下二阶严格双曲柯西问题的Gevrey适定性
DOI：
10.7146/math.scand.a-15063
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发表时间：
2008
影响因子：
0.5
通讯作者：
F. Hirosawa
中科院分区：
文献类型：
--
作者：
M. Cicognani;F. Hirosawa
研究了一类二阶严格双曲型方程在时间区间$[0,T]$上的后向柯西问题解的正则性丧失问题，该方程的时变系数仅在终点$t=0$有奇异性。本文的主要目的是证明解在Gevrey尺度上的正则性的丧失可以用$(0,T]$上各系数的可微阶、各导数的奇异阶（$t\to0$）和$(0,T)$上的一个积分描述的振荡振幅的稳定条件来描述。此外，我们通过构造一个反例，证明了$(0,T]$上$C^\infty$系数条件的最优性。
We consider the loss of regularity of the solution to the backward Cauchy problem for a second order strictly hyperbolic equation on the time interval $[0,T]$ with time depending coefficients which have a singularity only at the end point $t=0$. The main purpose of this paper is to show that the loss of regularity of the solution on the Gevrey scale can be described by the order of differentiability of the coefficients on $(0,T]$, the order of singularities of each derivatives as $t\to0$ and a stabilization condition of the amplitude of oscillations described by an integral on $(0,T)$. Moreover, we prove the optimality of the conditions for $C^\infty$ coefficients on $(0,T]$ by constructing a counterexample.
影响因子：
2.4
作者：
F. Hirosawa
通讯作者：
F. Hirosawa