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Main Title: On a multivalued differential equation with nonlocality in time
Author(s): Eikmeier, André
Emmrich, Etienne
Type: Article
Abstract: The initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a Volterra integral operator in time of convolution type with exponential decay. The two operators act on different Banach spaces where one is not embedded in the other. The set-valued right-hand side is measurable and satisfies certain continuity and growth conditions. Existence of a solution is shown via a generalisation of the Kakutani fixed-point theorem.
Subject(s): differential inclusion
exponentially decaying memory
Kakutani fixed-point theorem
monotone operator
multivalued differential equation
nonlinear evolution equation
volterra operator
Issue Date: 5-May-2020
Date Available: 4-Mar-2021
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: TU Berlin, Open-Access-Mittel – 2020
DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzepte
Journal Title: Vietnam Journal of Mathematics
Publisher: SpringerNature
Volume: 48
Issue: 4
Publisher DOI: 10.1007/s10013-020-00412-4
Page Start: 703
Page End: 718
EISSN: 2305-2228
ISSN: 2305-221X
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Numerische Analysis partieller Differentialgleichungen
Appears in Collections:Technische Universität Berlin » Publications

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