一个空间变量的2×2拟线性双曲组解的几何爆破

Geometric Blowup of 2×2 Quasilinear Systems in One Space Dimension

为研究拟线性双曲组解的生命跨度及爆破机制 ,S.Alinhac对一般的拟线性方程组引入了“几何爆破”的概念 ,并给出了爆破组。 S.Alinhac对于一个空间变量的 2× 2拟线性齐次严格双曲组证明了解的几何爆破机制。在一般的条件下 ,对于一个空间变量的 2× 2拟线性非齐次严格双曲组的 Cauchy问题 ,通过一定的技巧证明了经典解的几何爆破 ,并推广了 S.Alinhac的一些结果。

In order to study lifespan and blowup mechanism of the quasilinear hyperbolic system solution, S.Alinhac introduces the idea of 'geometric blowup' for general quasilinear system and gives blowup system. At the same time, he proves geometric blowup mechanism for 2×2 quasilinear homogeneous strictly hyperbolic systems in one space dimension. Under general condition, geometric blowup of classical solution is proved in this paper by using some skill for 2×2 quasilinear nonhomogeneous strictly hyperbolic systems in one space dimension, and some results of S.Alinhac′ s are extended.