拟线性双曲方程的两种Blowup机制

Two Kinds of Blowup Mechanism of Quasilinear Hyperbolic System

对于一般的初值 ,拟线性双曲方程不一定存在整体经典解 ,若不存在整体经典解 ,则解在有限时间内 blowup。主要考虑几种特殊的 Burgers方程 ,讨论其经典解的存在区间以及解发生 blowup时 ,几何blowup与常微 blowup之间的先后顺序。

For general initial value, quasilinear hyperbolic system does not always involves the whole classical solution. If there is no whole classical solution, solution blows up in finite time. This paper mostly considers some kinds of special Burgers equation and discusses lifespan of its classical solution and order between geometric blowup and ordinary differential blowup when solution blows up.