论文标题
在快速反应极限内，莱斯加环的凯勒·罗比诺模型的解决方案的有条件唯一性
Conditional uniqueness of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit
论文作者
论文摘要
我们研究了Hilhorst等人介绍的Liesegang环的Keller和Rubinow模型快速反应极限的弱解决方案的唯一性问题。 （J. Stat。Phys。135，2009，第107-132页）。该模型的特征是不连续的反应项，可以看作是空间分布的非理想中继磁滞的实例。通常，这种模型的解决方案的独特性是在某些横向条件下的条件。对于此处研究的模型，我们对降水边界进行了明确的描述，该描述引起了两种情况，以实现非唯一性，我们将其称为“自发降水”和“纠缠”。在弱解决方案的概念中，可以通过额外的，物理上合理的标准轻松忽略自发降水。第二种情况是一种情况，即在其共同的降水边界上的某个点的任何邻域都不能排序两个不同解决方案的降水界。我们表明，对于有限的时间间隔，解决方案是独一无二的。除此之外，独特的延续还要处于空间或时间横向条件。时间横向条件采用与具有不连续反应项的简单多组分半线性颂歌相同的形式。
We study the question of uniqueness of weak solution to the fast reaction limit of the Keller and Rubinow model for Liesegang rings as introduced by Hilhorst et al. (J. Stat. Phys. 135, 2009, pp. 107-132). The model is characterized by a discontinuous reaction term which can be seen as an instance of spatially distributed non-ideal relay hysteresis. In general, uniqueness of solutions for such models is conditional on certain transversality conditions. For the model studied here, we give an explicit description of the precipitation boundary which gives rise to two scenarios for non-uniqueness, which we term "spontaneous precipitation" and "entanglement". Spontaneous precipitation can be easily dismissed by an additional, physically reasonable criterion in the concept of weak solution. The second scenario is one where the precipitation boundaries of two distinct solutions cannot be ordered in any neighborhood of some point on their common precipitation boundary. We show that for a finite, possibly short interval of time, solutions are unique. Beyond this point, unique continuation is subject to a spatial or temporal transversality condition. The temporal transversality condition takes the same form that would be expected for a simple multicomponent semilinear ODE with discontinuous reaction terms.
