TVD (Totoal Variation Dimishing)
弱解定义
初始条件为$u(x,0)=u_0$的守恒律方程$u_t+f(u)x=0$，其弱解$u(x,t)$满足：对于任意的测试函数(test function) $\phi\in C_c^1(\mathbf{R}\times\mathbf{R})$, [\int_0^{\infty}\int_{-\infty}^{\infty}[\phi_t u +\phi_xf(u)]dxdt=-\int_{-\infty}^{\infty}\phi(x,0)u_0(x)dx.]
推导
黎曼问题(Riemann Problem)
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