Naslov
Heat equation as a Friedrichs system

Autori
Antonić, Nenad ; Burazin, Krešimir ; Vrdoljak Marko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Topics in PDE, Microlocal and Time-frequency Analysis / - Novi Sad, 2012, 18-18

Skup
Topics in PDE, Microlocal and Time-frequency Analysis

Mjesto i datum
Novi Sad, Srbija, 03.09.2012. - 08.09.2012

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Symmetric positive systems ; Heat equation

Sažetak
Symmetric positive systems (Friedrichs systems) of fi rst-order linear partial di erential equations were introduced by Kurt Otto Friedrichs (1958) in order to treat the equations that change their type, like the equations modelling transonic fluid flow. Such a system should be supplemented by an admissible boundary condition. Friedrichs showed that this class of problems encompasses a wide variety of classical and neoclassical initial and boundary value problems for various linear partial di erential equations. Inspired by recent advances in the general theory of Friedrichs' systems, we apply the newly developed results to the heat equation, by showing how the intrinsic theory of Ern, Guermond and Caplain (2007) can be used in order to get a well-posedness result for the Dirichlet initial- boundary value problem. We also demonstrate the application of the two- field theory with partial coercivity of Ern and Guermond (2008), originally developed for elliptic problems, and also discuss di fferent possibilities for the construction of an appropriate boundary operator.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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