Wave Equation for Sturm-Liouville Operator with Singular Intermediate Coefficient and Potential
Wave Equation for Sturm-Liouville Operator with Singular Intermediate Coefficient and Potential
复制标题
具有奇异中间系数和势的Sturm-Liouville算子的波动方程
DOI：
10.1007/s40840-023-01587-y
复制
发表时间：
2023
影响因子：
1.2
通讯作者：
Ruzhansky M
中科院分区：
文献类型：
--
作者：
Ruzhansky M
本文考虑有界区域上的波动方程，其Sturm-Liouville算子具有奇异中间系数和奇异位势。为了获得和评估的解决方案，分离的变量的方法被使用，然后在傅立叶级数的Sturm-Liouville算子的本征函数的展开被使用。Sturm-Liouville本征函数由使用修改的Prufer变换的这些系数确定。证明了具有奇异系数的波动方程很弱解的存在唯一性和相容性定理。
In this paper, we consider a wave equation on a bounded domain with a Sturm–Liouville operator with a singular intermediate coefficient and a singular potential. To obtain and evaluate the solution, the method of separation of variables is used, then the expansion in the Fourier series in terms of the eigenfunctions of the Sturm–Liouville operator is used. The Sturm–Liouville eigenfunctions are determined by such coefficients using the modified Prufer transform. Existence, uniqueness and consistency theorems are also proved for a very weak solution of the wave equation with singular coefficients.