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

• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540201/
• 关键词: Kirchhhoff方程式; 消散型双曲型方程式; Kirchhiff型方程式; Kirchhoff方程式; 消散項; 漸近挙動; 大域解

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.

我们考虑了随着耗散的耗散kirchhoff方程，耗散的系数在有价值的时间上衰减。首先，我们考虑耗散的kirchhoff方程，其中耗散项的系数取决于时间和空间的贵重物质和衰减，而相比，相对于有价值的时间而言。然后，我们证明了具有小Sobolev Norm的初始数据的解决方案的独特全局存在。其次，我们考虑了耗散的基尔chhoff方程，其中耗散项的系数仅取决于迅速衰减的时间。然后，我们展示了某些函数类别上散射的独特全局溶解度和存在。