| 祝雪,杨晗.带对数阻尼项的对数型类波方程解的整体存在性与爆破[J].数学年刊A辑,2023,44(4):335~352 |
| 带对数阻尼项的对数型类波方程解的整体存在性与爆破 |
| Global Existence and Blow-up of Solutions to a Logarithmic-Type Wave Equation with Logarithmic Damping Term |
| Received:March 30, 2023 Revised:September 11, 2023 |
| DOI：10.16205/j.cnki.cama.2023.0024 |
| 中文关键词: 对数型类波方程, 对数阻尼项, 柯西问题, 整体解, 爆破 |
| 英文关键词:Logarithmic-Type wave equation, Logarithmic damping term,Cauchy problem, Global solution, Blow-up |
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| 中文摘要: |
| 本文研究一类带对数阻尼项的对数型类波方程的柯西问题, 考虑对数阻尼项对解存在性的影响.通过~Fourier 变换、Laplace 变换及~Young 不等式建立了线性问题解的衰减估计. 在恰当的工作空间中,利用整体迭代方法证明了解的整体存在唯一性; 利用测试函数方法得到了解的有限时刻爆破. |
| 英文摘要: |
| In this paper, the authors study the Cauchy problem of a logarithmic-type wave equation with logarithmic damping term, and consider the influence of the logarithmic damping term on the existence of solutions. Through Fourier transform, Laplace transform and Young′s inequality, the decay estimation of the solution of the linear problem is established. In an appropriate working space, the global existence and uniqueness of the solution to above Cauchy problem is proved by utilizing the global iteration method, and the finite time blow-up of the solution is obtained by means of the test function method. |
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