论文标题
不连续的扩散传输方程的速度平均速度
Velocity averaging for diffusive transport equations with discontinuous flux
论文作者
论文摘要
我们考虑具有不连续通量的扩散传输方程，并证明在非分类条件下的速度平均结果。为了实现结果，我们引入了一个新的微局部缺陷功能的新变体，该功能能够``识别''方程类型的变化。作为推论，我们表明存在与不连续通量的非线性退化抛物线方程的库奇问题的弱解决方案。我们还显示了在扩散项下非分类条件下，在非分类条件下，在$ t = 0 $中存在$ t = 0 $的存在。
We consider a diffusive transport equation with discontinuous flux and prove the velocity averaging result under non-degeneracy conditions. In order to achieve the result, we introduce a new variant of micro-local defect functionals which are able to ``recognise'' changes of the type of the equation. As a corollary, we show the existence of a weak solution for the Cauchy problem for nonlinear degenerate parabolic equation with discontinuous flux. We also show existence of strong traces at $t=0$ for so-called quasi-solutions to degenerate parabolic equations under non-degeneracy conditions on the diffusion term.
