Generalized fourier transforms and global small solutions to kirchhoff equations
Generalized fourier transforms and global small solutions to kirchhoff equations
复制标题
广义傅立叶变换和基尔霍夫方程的全局小解
DOI：
10.1080/00036819508840364
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
R. Racke
中科院分区：
文献类型：
--
作者：
R. Racke
证明了与适当的紧支势相关联的广义傅里叶变换的逆映射到快减函数空间。这是用于研究波动方程的非局部非线性的类型是一个外部区域在R3与V = 0，假设Dirichlet边界条件u。对于一类光滑数据，我们得到了小解的整体存在性，以及当t→∞时渐近行为的部分特征.本文还研究了方程的负特征值所对应的特征向量所生成的整体大解的存在性。
It is proved that the inverse of the generalized Fourier transform associated to V an appropriate compactly supported potential, maps into the space of rapidly decreasing functions. This is used for the study of wave equations with non-local nonlinearities of the type being an exterior domain in R3 with V = 0, assuming Dirichlet boundary conditions for u. For a class of smooth data we obtain global existence of small solutions, as well as a partial characterization of the asymptotic behavior as t→∞ . The existence of global large solutions generated by eigenvectors corresponding to negative eigenvalues of is also investigated.