论文标题
一类线性演化方程的独特解决方案类别
Uniqueness class of solutions to a class of linear evolution equations
论文作者
论文摘要
在本文中，我们研究了无限图上的波方程。一方面，与歧管上的波方程相反，我们构建了一个示例图形上波动方程的cauchy问题的示例。另一方面，我们获得了波动方程解的鲜明独特性类别。结果是从唯一性类别中的溶液的时间分析到波方程的时间。在最后一部分中，我们将结果扩展到一类线性演化方程。
In this paper, we study the wave equation on infinite graphs. On one hand, in contrast to the wave equation on manifolds, we construct an example for the non-uniqueness for the Cauchy problem of the wave equation on graphs. On the other hand, we obtain a sharp uniqueness class for the solutions of the wave equation. The result follows from the time analyticity of the solutions to the wave equation in the uniqueness class. In the last part, we extend the result to a wide class of linear evolution equations.
