Derivative loss for Kirchhoff equations with non-Lipschitz nonlinear term
Derivative loss for Kirchhoff equations with non-Lipschitz nonlinear term
复制标题
具有非 Lipschitz 非线性项的 Kirchhoff 方程的导数损失
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Massimo Gobbino
中科院分区：
文献类型：
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作者：
M. Ghisi;Massimo Gobbino
本文考虑具有连续非线性项的抽象Kirchhoff方程的柯西边值问题m：[0，+\inty)-->；[0，+\inty].众所周知，只要初始数据足够规则，就存在局部解。所需的正则性取决于m的连续模.本文给出一些反例，以说明存在结果中所要求的正则性是尖锐的，至少当我们想要解具有与初始数据相同的空间正则性时是这样.在这些例子中，我们构造的局部解在t=0时确实是正则的，但在空间变量中表现出瞬时(通常是无限的)导数损失。
In this paper we consider the Cauchy boundary value problem for the abstract Kirchhoff equation with a continuous nonlinearity m : [0,+\infty) --> [0,+\infty). It is well known that a local solution exists provided that the initial data are regular enough. The required regularity depends on the continuity modulus of m. In this paper we present some counterexamples in order to show that the regularity required in the existence results is sharp, at least if we want solutions with the same space regularity of initial data. In these examples we construct indeed local solutions which are regular at t = 0, but exhibit an instantaneous (often infinite) derivative loss in the space variables.
影响因子：
2.4
作者：
F. Hirosawa
通讯作者：
F. Hirosawa