NDLI: Non-Stationary Abstract Friedrichs Systems

Content Provider	Springer Nature Link
Author	Erceg, Marko Burazin, Krešimir
Copyright Year	2016
Abstract	Inspired by the results of Ern et al. (Commun Partial Differ Equ 32:317–341, 2007) on the abstract theory for Friedrichs symmetric positive systems, we give the existence and uniqueness result for the initial- (boundary) value problem for the non-stationary abstract Friedrichs system. Despite the absence of the well-posedness result for such systems, there were already attempts for their numerical treatment by Burman et al. (SIAM J Numer Anal 48:2019–2042, 2010) and Bui-Thanh et al. (SIAM J Numer Anal 51:1933–1958, 2013). We use the semigroup theory approach and prove that the operator involved satisfies the conditions of the Hille–Yosida generation theorem. We also address the semilinear problem and apply the new results to a number of examples, such as the symmetric hyperbolic system, the unsteady div–grad problem, and the wave equation. Special attention was paid to the (generalised) unsteady Maxwell system.
Ending Page	3796
Page Count	20
Starting Page	3777
File Format	PDF
ISSN	16605446
e-ISSN	16605454
Journal	Mediterranean Journal of Mathematics
Issue Number	6
Volume Number	13
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-04-13
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	abstract Cauchy problem Initial-boundary value problems for nonlinear first-order equations One-parameter semigroups and linear evolution equations Symmetric positive first-order system Differential equations in abstract spaces Linear first-order systems semigroup General (adjoints, conjugates, products, inverses, domains, ranges, etc.) Mathematics Initial value problems for linear first-order systems
Content Type	Text
Resource Type	Article
Subject	Mathematics

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