论文标题
周期性单周脉冲方程的全球可允许保守弱解决方案的存在和独特性
The existence and uniqueness of global admissible conservative weak solution for the periodic single-cycle pulse equation
论文作者
论文摘要
本文致力于研究周期性单周脉冲方程的全球可允许保守弱解的存在和独特性。我们首先通过引入一组新的变量来将方程式转换为等效的半线性系统。使用标准的普通微分方程理论，我们获得了半线性系统的全局解决方案。接下来，返回原始坐标，我们为周期性的单周脉冲方程提供了全局可允许的保守弱解决方案。最后，鉴于一个可接受的保守弱解决方案，我们找到一个方程式，可以通过每个初始点挑出独特的特征曲线，并证明全球可允许的保守弱解决方案的独特性，而没有任何其他假设。
This paper is devoted to the study of the existence and uniqueness of global admissible conservative weak solutions for the periodic single-cycle pulse equation. We first transform the equation into an equivalent semilinear system by introducing a new set of variables. Using the standard ordinary differential equation theory, we then obtain the global solution to the semilinear system. Next, returning to the original coordinates, we get the global admissible conservative weak solution for the periodic single-cycle pulse equation. Finally, given an admissible conservative weak solution, we find a equation to single out a unique characteristic curve through each initial point and prove the uniqueness of global admissible conservative weak solution without any additional assumptions.
