具有奇异耗散项的Burger's方程整体光滑解的存在性

Existence of global smooth solution to Burger's equation with singular dissipation

考虑到了在 x =0处具有奇性的带耗散项的 Burger' s方程ut+f ( u) x =g( u)x的初边值问题整体光滑解的存在性 ,利用一个函数变换 ,我们将上式转化成一个没有奇性的双曲型方程 ,然后应用特征线法 ,获得了相应问题的 C1 -模估计 ,从而得到了初边值问题整体光滑解的存在性 .

In this paper, we consider the existence of global smooth solution to initial bounday value problem to Burger's equation with sigular dissipationu t+f(u) x=-g(u)x.Applying a function transformation, we transform it into a regular hyperbolic equation. Then, by using the characteristic method, we obtian C 1 norm estimates to the corresponding progblem and prove the existence of global smooth solution to the initial boundary value problem.