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

^*Corresponding author for this work

Research output: Contribution to journal › Conference article in Journal › Research › peer-review

2 Citations (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.

Original language	English
Book series	IFAC-PapersOnLine
Volume	48
Pages (from-to)	587-592
Number of pages	6
ISSN	2405-8963
DOIs	https://doi.org/10.1016/j.ifacol.2015.09.250
Publication status	Published - 1 Jul 2015
Event	1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, MICNON 2015 - Saint Petersburg, Russian Federation Duration: 24 Jun 2015 → 26 Jun 2015

Conference

Conference	1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, MICNON 2015
Country/Territory	Russian Federation
City	Saint Petersburg
Period	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

Keywords

Heat equation
Parabolic PDE
Stability analysis
State-dependent parameters

Access to Document

10.1016/j.ifacol.2015.09.250

AUB Link

Search for the material in Aalborg University Library's search engine

Cite this

@inproceedings{6a0b5a21cec6470190ebac77f53c96f7,

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",

}

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

Abstract

Conference

Keywords

Access to Document

AUB Link

Other files and links

Fingerprint

Cite this