Invariance and strict invariance for nonlinear evolution problems with applications. (May 2022)

• Record Type: Journal Article
• Authors: Ćwiszewski, Aleksander; Gabor, Grzegorz; Kryszewski, Wojciech
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: primary 37L05 -- secondary 47H06 47J35 35K91; Evolution equation -- Invariance -- Strict invariance -- PDEs -- Accretive operator; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112756
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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 constraining functional are expressed in terms of the Dini derivative of that functional, outside the considered set in directions determined by the considered m -accretive operator. An approach for non-reflexive Banach spaces is developed and some result improving a recent paper (Cannarsa et al., 2018) is presented. Applications to nonlinear obstacle problems and age-structured population models are presented in spaces of continuous functions where an advantage of such approach is taken. Moreover, some new abstract criteria for the so-called strict invariance are derived and their direct application to problems with barriers is discussed.