论文标题
一阶的分析式准差分方程解决方案的最大结构域
Maximal domains of solutions for analytic quasilinear differential equations of first order
论文作者
论文摘要
我们研究了标量函数的第一阶的准线性部分微分方程的库奇问题，研究了局部实质分析解决方案的实地延续。通过使用特征向量场的第一积分和隐式函数定理，我们确定了局部解决方案作为单值函数的分析扩展的最大结构域。我们提供了一些示例，包括承认全球第一积分的标量保护法，以便我们的方法适用。
We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.
