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Asymptotic behavior and singular limit problem for dissipative hyperbolic equations

耗散双曲方程的渐近行为和奇异极限问题

基本信息

批准号：
21540201
负责人：
YAMAZAKI Taeko
金额：
$ 1.33万
依托单位：
Tokyo University of Science
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2009
资助国家：
日本
起止时间：
2009 至 2011
项目状态：
已结题

项目摘要

We considered dissipative Kirchhoff equation with dissipation, where the coefficient of the dissipation decays with respect to the time valuable. First we consider dissipative Kirchhoff equation where the coefficient of the dissipation term depends time and space valuables and decays slowly than the critical exponent with respect to the time valuable. Then we proved the unique global existence of the solution for initial data with small Sobolev norm. Secondly we considered the dissipative Kirchhoff equation where the coefficient of the dissipation term depends only on time valuable which decays rapidly. Then we showed the unique global solvability and existence of the scattering on some class of the functions.

考虑了耗散的Kirchhoff方程，其中耗散系数随时间衰减。首先我们考虑耗散的Kirchhoff方程，其中耗散项的系数依赖于时间和空间值，并且相对于时间值比临界指数衰减得慢。然后证明了在小Sobolev范数下解的唯一整体存在性。其次，我们考虑了耗散Kirchhoff方程，其中耗散项的系数只依赖于时间值，衰减很快。然后证明了一类函数的唯一整体可解性和散射的存在性。