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On Local Stability of Equilibrium Profiles of Nonisothermal Axial Dispersion Tubular Reactors ?

机译：关于非等温轴向分散管式反应器平衡型材的局部稳定性

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Exponential (exp.) stability of equilibrium profiles for a nonisothermal axial dispersion tubular reactor is considered. This model is described by nonlinear partial differential equations (PDEs) whose state components are the temperature, the reactant and the product concentrations inside of the reactor. It is shown how to get appropriate local exponential stability of the equilibria for the nonlinear model, on the basis of stability properties of its linearized version and some relaxed Fréchet differentiability conditions of the nonlinear semigroup generated by the dynamics. In the case where the reactor can exhibit only one equilibrium profile, the latter is always locally exponentially stable for the nonlinear system. When three equilibria are highlighted, local bistability is established, i.e. the pattern (locally) "(exp.) stable - unstable - (exp.) stable" holds. The results are illustrated by some numerical simulations. As perspectives, the concept of state feedback is also used in order to show a manner to stabilize exponentially a nonlinear system on the basis of its capacity to stabilize exponentially a linearized version of the nonlinear dynamics and some Fréchet differentiability conditions of the corresponding closed-loop nonlinear semigroup.
机译：考虑指数（EXP。）考虑了非等热轴向分散管式反应器的平衡轮廓的稳定性。该模型由非线性部分微分方程（PDE）描述，其状态分量是温度，反应物和反应器内的产物浓度。它示出了如何基于其线性化版本的稳定性特性以及由动态产生的非线性半群的一些轻松的Fréchet可怜条件的稳定性特性获得适当的局部指数稳定性。在反应器只能表现出一个平衡曲线的情况下，后者对于非线性系统总是局部呈指数稳定的。当突出三个均衡时，建立局部双稳态，即模式（本地）“（exp.）稳定 - （exp。）稳定”持有。结果由一些数值模拟说明。作为透视图，还使用状态反馈的概念，以便在其能力稳定非线性系统的基础上稳定非线性系统的能力，以稳定指数的非线性动态的能力和相应的闭环的一些FRéchet可微分条件的能力稳定非线性系统的方式非线性半群。

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