论文标题
关于退化的非线性扩散方程的Riemann问题弱解决方案的结构
On the structure of weak solutions to the Riemann problem for degenerate nonlinear diffusion equation
论文作者
论文摘要
我们发现，对于分段恒定扩散系数的退化半线性抛物线方程的Riemann问题的明确形式。证明相变线（自由边界）对应于有限数量变量的某些严格凸功能的最小点。在阶段数量倾向于无限的限制中，我们获得了具有任意非负扩散函数的自相似溶液的变异公式。
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to the minimum point of some strictly convex function of a finite number of variables. In the limit as number of phases tend to infinity we obtain a variational formulation of self-similar solution with an arbitrary nonnegative diffusion function.
