论文标题
应用程序的非线性演化问题的不变性和严格的不变性
Invariance and Strict Invariance for Nonlinear Evolution Problems with Applications
论文作者
论文摘要
提供（可能是非线性）$ m $ $ accretive操作员扰动所控制的进化问题的足够条件。根据该功能的DINI衍生物表示，相对于一个约束功能的超级级别集的条件以外的dini衍生物表示，在由管理$ M $ -ACCRETIVE运算符确定的方向上被考虑的sublevel集合。开发了一种非反射性Banach空间的方法，有些结果改善了最近的论文[P. Cannarsa，G。DaPrato，H。Frankowska，Banach空间中准散文系统的不变性。 J. Math。肛门。应用程序。提出了457（2018），1173-1187]。在采用该方法优势的连续功能的空间中，介绍了在非线性障碍问题和年龄结构的人群模型中的应用。此外，得出了一些关于所谓严格不变性的新的抽象标准，并显示了它们在障碍问题上的直接应用。
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint functional are expressed in terms of the Dini derivative of that functional, outside the considered sublevel set in directions determined by the governing $m$-accretive operator. An approach for non-reflexive Banach spaces is developed and some result improving a recent paper [P. Cannarsa, G. Da Prato, H. Frankowska, Invariance of quasi-dissipative systems in Banach spaces. J. Math. Anal. App. 457 (2018), 1173-1187] is presented. Applications to nonlinear obstacle problems and age-structured population models are presented in spaces of continuous functions where advantages of that approach are taken. Moreover, some new abstract criteria for the so-called strict invariance are derived and their direct applications to problems with barriers are shown.
