论文标题
LIFSHITZ-SLYOZOV方程的初始有限值问题，边界的非平滑速率
The Initial-boundary value problem for the Lifshitz-Slyozov equation with non-smooth rates at the boundary
论文作者
论文摘要
我们证明了lifshitz--slyozov方程（半线上的非线性传输方程）的解决方案解决方案的存在和唯一性，重点介绍了具有原点的无界导数的动力学速率的情况。我们的理论尤其涵盖了那些以速率为原点的速率行为的情况，为此，人们需要施加流入行为和描述成核现象的边界条件。我们在这里介绍的方法证明存在是基于特征的公式，对奇异边界附近的行为进行了仔细的分析。作为副产品，我们提供了在半线上的线性连续性方程的一般理论，其运输场在边界处退化。我们还谈到了流入解决方案对LifShitz--Slyozov模型的最大和独特性，从而利用了相关传输方程的单调性能。
We prove existence and uniqueness of solutions to the initial-boundary value problem for the Lifshitz--Slyozov equation (a nonlinear transport equation on the half-line), focusing on the case of kinetic rates with unbounded derivative at the origin. Our theory covers in particular those cases with rates behaving as power laws at the origin, for which an inflow behavior is expected and a boundary condition describing nucleation phenomena needs to be imposed. The method we introduce here to prove existence is based on a formulation in terms of characteristics, with a careful analysis on the behavior near the singular boundary. As a byproduct we provide a general theory for linear continuity equations on a half-line with transport fields that degenerate at the boundary. We also address both the maximality and the uniqueness of inflow solutions to the Lifshitz--Slyozov model, exploiting monotonicity properties of the associated transport equation.
