论文标题
具有单数中间系数和电势的Sturm-Liouville操作员的波程
Wave equation for Sturm-Liouville operator with singular intermediate coefficient and potential
论文作者
论文摘要
在本文中，我们考虑了一个有界域上的波动方程，该域具有带有奇异中间系数和奇异电势的Sturm-Liouville操作员。为了获得和评估解决方案，使用了变量分离的方法，然后使用Sturm-liouville操作员的特征函数来傅立叶系列中的扩展。 Sturm-liouville本征函数由使用改良的Prufer变换来确定此类系数。对于具有单数系数的波动方程非常弱的解决方案，也证明存在，唯一性和一致性定理。
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.
