Stability properties of a heat equation with state-dependent parameters and asymmetric boundary conditions

Christoph Josef Backi*, Jan Dimon Bendtsen, John Leth, Jan Tommy Gravdahl

*Kontaktforfatter

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1 Citation (Scopus)

Resumé

In this work the stability properties of a partial differential equation (PDE) with state-dependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show that the PDE converges to a stationary solution given by (fixed) boundary conditions which explicitly diverge from each other. Numerical simulations illustrate the results.

OriginalsprogEngelsk
BogserieIFAC-PapersOnLine
Vol/bind48
Sider (fra-til)587-592
Antal sider6
ISSN2405-8963
DOI
StatusUdgivet - 1 jul. 2015
Begivenhed1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, MICNON 2015 - Saint Petersburg, Rusland
Varighed: 24 jun. 201526 jun. 2015

Konference

Konference1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, MICNON 2015
LandRusland
BySaint Petersburg
Periode24/06/201526/06/2015
Sponsoret al., International Federation of Automatic Control (IFAC) - Technical Committee on Adaptive and Learning Systems, International Federation of Automatic Control (IFAC) - Technical Committee on Modeling, Identification and Signal Processing, International Federation of Automatic Control (IFAC) - Technical Committee on Networked Systems, International Federation of Automatic Control (IFAC) - Technical Committee on Non-Linear Control Systems, International Federation of Automatic Control (IFAC) - Technical Committee on Optimal Control

Fingerprint

Partial differential equations
Boundary conditions
Temperature distribution
Computer simulation
Hot Temperature

Citer dette

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title = "Stability properties of a heat equation with state-dependent parameters and asymmetric boundary conditions",
abstract = "In this work the stability properties of a partial differential equation (PDE) with state-dependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show that the PDE converges to a stationary solution given by (fixed) boundary conditions which explicitly diverge from each other. Numerical simulations illustrate the results.",
keywords = "Heat equation, Parabolic PDE, Stability analysis, State-dependent parameters",
author = "Backi, {Christoph Josef} and Bendtsen, {Jan Dimon} and John Leth and Gravdahl, {Jan Tommy}",
year = "2015",
month = "7",
day = "1",
doi = "10.1016/j.ifacol.2015.09.250",
language = "English",
volume = "48",
pages = "587--592",
journal = "I F A C Workshop Series",
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Stability properties of a heat equation with state-dependent parameters and asymmetric boundary conditions. / Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John; Gravdahl, Jan Tommy.

I: IFAC-PapersOnLine, Bind 48, 01.07.2015, s. 587-592.

Publikation: Bidrag til tidsskriftKonferenceartikel i tidsskriftForskningpeer review

TY - GEN

T1 - Stability properties of a heat equation with state-dependent parameters and asymmetric boundary conditions

AU - Backi, Christoph Josef

AU - Bendtsen, Jan Dimon

AU - Leth, John

AU - Gravdahl, Jan Tommy

PY - 2015/7/1

Y1 - 2015/7/1

N2 - In this work the stability properties of a partial differential equation (PDE) with state-dependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show that the PDE converges to a stationary solution given by (fixed) boundary conditions which explicitly diverge from each other. Numerical simulations illustrate the results.

AB - In this work the stability properties of a partial differential equation (PDE) with state-dependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show that the PDE converges to a stationary solution given by (fixed) boundary conditions which explicitly diverge from each other. Numerical simulations illustrate the results.

KW - Heat equation

KW - Parabolic PDE

KW - Stability analysis

KW - State-dependent parameters

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DO - 10.1016/j.ifacol.2015.09.250

M3 - Conference article in Journal

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EP - 592

JO - I F A C Workshop Series

JF - I F A C Workshop Series

SN - 1474-6670

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