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.

我们考虑了具有耗散的耗散基尔霍夫方程，其中耗散系数随时间价值而衰减。首先，我们考虑耗散基尔霍夫方程，其中耗散项的系数取决于时间和空间价值，并且相对于时间价值比临界指数衰减慢。然后我们证明了具有小Sobolev范数的初始数据解的唯一全局存在性。其次，我们考虑了耗散基尔霍夫方程，其中耗散项的系数仅取决于快速衰减的时间价值。然后我们展示了该函数在某类函数上的独特的全局可解性和散射的存在性。