SIAM Review, Volume 62, Issue 1, Page 1-1, January 2020.
Bernard Brogliato and Aneel Tanwani are the authors of “Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability,” the Survey and Review paper in this issue. To get a feeling for the problems being dealt with, the reader may have a look at the electrical circuit in Figure 4.1(c) (also shown on the cover). Kirchhoff's voltage law yields (L\dot x = -Rx+łambda); (x) is the current through the resistor, and (L\dot x), (-Rx) and (łambda) are, respectively, the drops in voltage across the inductor, the resistor, and the diode. This would be a differential equation for (x) if (łambda) were a known function of (x), which it isn't. For any (łambda >0), i.e., whenever the voltage at the cathode is higher than at the anode, the (ideal) diode does not conduct, which implies that (x) coincides with the current (i) from the source. Therefore when (x) takes the value (i), all we can say about (łambda) is that it lies in the set ((0,\infty)). We have encountered an equation of the general format studied in the paper: (\dot x = f(t,x)+G(t,x)), \(x\in\mathbb R^n\), (w\in\mathbb R^m), where (w) is required to belong to a set (-a̧l F(t,Hx,Jw)) ((G), (H), and (J) are matrices). The diode circuit also illustrates the concept of complementarity: either the diode does not conduct ((łambda >0) and (x-i=0)) or it does, and then (łambda = 0), (x-i>0). Similar complementarity problems are frequent in mechanics; a bouncing ball either has a positive height and gets no force from the floor or has zero height and then receives an upward reaction force. In addition to complementarity problems, the general format in the paper includes sweeping processes, maximal monotone differential equations, evolution inequalities, and additional related formalisms. The authors describe numerous applications to electrical circuits, mechanical systems, and other fields. With 592 references and five appendices that provide mathematical background, the article has much to offer those interested in an area that is certainly important in modeling.

中文翻译：

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调查和审查

SIAM评论，第62卷，第1期，第1-1页，2020年1月。
Bernard Brogliato和Aneel Tanwani是本期《调查与评论》论文“与单调集值算子耦合的动力系统：形式主义，应用，良好的定位性和稳定性”的作者。为了感觉到正在处理的问题，读者可以看一下图4.1（c）中的电路（也显示在封面上）。基尔霍夫的电压定律产生（L \ dot x = -Rx +łambda）; （x）是流经电阻的电流，（L \ x），（-Rx）和（łambda）分别是电感，电阻和二极管两端的电压降。如果（λambda）是（x）的已知函数，则不是（x）的微分方程。对于任何（λambda> 0），即，只要阴极上的电压高于阳极上的电压，（理想）二极管就不会导通，这意味着（x）与源电流（i）一致。因此，当（x）取值（i）时，我们可以说的关于（łambda）在于它位于集合（（0，\ infty））中。我们遇到了本文研究的一般格式的方程：（\ dot x = f（t，x）+ G（t，x）），\（x \ in \ mathbb R ^ n \），（w \ in \ mathbb R ^ m），其中（w）必须属于集合（-a̧F（t，Hx，Jw））（（G），（H）和（J）是矩阵）。二极管电路还说明了互补性的概念：要么二极管不导通（（λambda> 0）且（xi = 0）），要么它导通，然后（λambda= 0）（xi> 0）。类似的互补性问题在力学中很常见。弹跳球的高度为正，没有从地板上受到的力，高度为零，然后受到向上的反作用力。除了互补性问题，本文的一般格式包括扫描过程，最大单调微分方程，演化不等式和其他相关形式主义。作者描述了在电路，机械系统和其他领域的大量应用。凭借592个参考资料和五个提供数学背景的附录，本文为那些对建模必不可少的领域感兴趣的人提供了很多东西。