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Main Title: On the smoothing property of linear delay partial differential equations
Author(s): Altmann, Robert
Zimmer, Christoph
Type: Research Paper
Abstract: We consider linear partial differential equations with an additional delay term, which - under spatial discretization - lead to ordinary differential equations with fixed delay of retarded type. This means that the semi-discrete solution gains smoothness over time. For the concept of classical, mild, and weak solutions we analyse whether this effect also takes place in the original system. We show that some systems behave in a neutral way only. As a result, the smoothness of the exact solution remains unchanged instead of gaining smoothness over time.
Subject(s): linear PDEs
delay differential equations
smoothing property
Issue Date: 7-Jul-2017
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 35B65 Smoothness and regularity of solutions of PDE
35R10 Partial functional-differential or differential-difference equations, with or without deviating arguments
65Q05 Difference and functional equations, recurrence relations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2017, 07
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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