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

作　　者：祝雪 杨晗[1] ZHU Xue;YANG Han(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China.)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《数学年刊（A辑）》2023年第4期335-352,共18页Chinese Annals of Mathematics

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.In this paper,the authors study the Cauchy problem of a logarithmic-type wave equation with logarithmic damping term,and consider the infuence 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.

关 键 词：对数型类波方程 对数阻尼项 柯西问题 整体解 爆破 

分 类 号：O175.29[理学—数学]