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

doi:10.1016/j.ifacol.2015.09.250

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

Publikation: Bidrag til tidsskrift › Konferenceartikel i tidsskrift › Forskning › peer review

2 Citationer (Scopus)

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.

Originalsprog	Engelsk
Bogserie	IFAC-PapersOnLine
Vol/bind	48
Sider (fra-til)	587-592
Antal sider	6
ISSN	2405-8963
DOI	https://doi.org/10.1016/j.ifacol.2015.09.250
Status	Udgivet - 1 jul. 2015
Begivenhed	1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, MICNON 2015 - Saint Petersburg, Rusland Varighed: 24 jun. 2015 → 26 jun. 2015

Konference

Konference	1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, MICNON 2015
Land/Område	Rusland
By	Saint Petersburg
Periode	24/06/2015 → 26/06/2015
Sponsor	et 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

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10.1016/j.ifacol.2015.09.250

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Citationsformater

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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 = jul,

day = "1",

doi = "10.1016/j.ifacol.2015.09.250",

language = "English",

volume = "48",

pages = "587--592",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "Elsevier",

note = "1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, MICNON 2015 ; Conference date: 24-06-2015 Through 26-06-2015",

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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

UR - http://www.scopus.com/inward/record.url?scp=84953872112&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2015.09.250

DO - 10.1016/j.ifacol.2015.09.250

M3 - Conference article in Journal

SN - 2405-8963

VL - 48

SP - 587

EP - 592

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

T2 - 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, MICNON 2015

Y2 - 24 June 2015 through 26 June 2015

ER -

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

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