一个奇异双曲型方程整体光滑解的存在性

Existence of global smooth solution to a hyperbolic equation with singularity

考虑了在x=0处具有奇性的拟线性双曲型方程ut+12 u2x=- u2x ( 1)的初边值问题整体光滑解的存在性 ,利用一个函数变换 ,将 ( 1)转化成一个没有奇性的双曲型方程 ,然后应用文献 [4 ],[5 ]建立的关于一阶拟线性双曲型方程组的极值原理的结果 ,获得相应问题解的C1 模估计 ,从而得到了初边值问题整体光滑解的存在性 .

This paper considers the existence of global smooth solution to initial boundary value problem to a quasilinear hyperbolic equationu t+(12u2) x=-u2x(1)with singularity at x=0 Applying a function transformation, it transforms (1) into a regular hyperbolic equation. Then, by using the maximum principle of the first order quasilinear hyperbolic system established by ,, it obtains C1-norm estimates to the corresponding problem and proves the existence of global smooth solution to the inital boundary value problem.