一阶拟线性双曲型方程组Goursat问题的整体经典解

Global Classical Solutions to the Goursat Problem for First-Order Quasilinear Hyperbolic Systems

考虑一阶拟线性双曲型方程组的Goursat问题,在方程组为弱线性退化的假设下,当在特征边界上给出的边界函数的C^1范数充分小且具有一定衰减性时,得到整体C^1解的存在唯一性,并给出该解的逐点估计.作为该结果的一个重要例子,将此结论应用于闵可夫斯基空间中的时向极值曲面方程.

We consider the Goursat problem for first-order quasilinear hyperbolic systems. Under the assumptions that the system is weakly linearly degenerate and the boundary conditions on the characteristics are small and decaying, we obtain the existence of global C1 solutions and give a pointwise estimate to classical solutions. As an important example, we apply this result to the equation for timelike extremal surface in Minkowski space.