一阶拟线性双曲型方程组Goursat问题经典解的破裂机制(英文)

Blow-up Mechanism of Classical Solutions to Goursat Problem for Quasilinear Hyperbolic Systems

对一阶拟线性双曲型方程组的Goursat问题,利用特征线方法及波分解公式,在方程组不是弱线性退化的假设下,当特征边界上给出的边界函数C1范数充分小、且满足一定衰减性时,得到其C1解的破裂机制及关于生命跨度的渐近估计.

Under the assumptions that the quasilinear hyperbolic system is not weakly linearly degenerate and the boundary functions given on the characteristic boundaries possess small C 1 norms and certain decaying properties, by using the characteristic method and the decomposition for waves, we obtain the blow-up mechanism and the asymptotic behavior of the life-span of the C 1 solution to the Goursat problem.