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

Authors

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

Type: Article

Publication Date: 2015-01-01

Citations: 2

DOI: https://doi.org/10.1016/j.ifacol.2015.09.250

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Abstract

In this work the stability properties of a partial differential equation (PDE) with statedependent 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.

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A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content. A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

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Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 27 October 2020Accepted: 22 July 2021Published online: 21 October 2021Keywordsbackward heat equation, Lipschitz … Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 27 October 2020Accepted: 22 July 2021Published online: 21 October 2021Keywordsbackward heat equation, Lipschitz stability, inverse problem, fluorescence microscopyAMS Subject Headings35B35, 35K05, 35R30Publication DataISSN (print): 0036-1410ISSN (online): 1095-7154Publisher: Society for Industrial and Applied MathematicsCODEN: sjmaah

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ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＦＯＲＳＥＭＩ－ＨＯＭＯＧＥＮＥＯＵＳＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＤｏｎｇＱｉｎｘｉ（董勤喜）；ＨｕａｎｇＸｉａｎｋａｉ（黄先开）（ＲｅｃｅｉｖｅｄＪｕｌｙ．４．１９... ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＦＯＲＳＥＭＩ－ＨＯＭＯＧＥＮＥＯＵＳＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＤｏｎｇＱｉｎｘｉ（董勤喜）；ＨｕａｎｇＸｉａｎｋａｉ（黄先开）（ＲｅｃｅｉｖｅｄＪｕｌｙ．４．１９...

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

Authors

Abstract

Locations

Dynamic time step and stability criteria comparison for the heat diffusion equation

Dynamic time step and stability criteria comparison for the heat diffusion equation

STABILITY OF DIFFERENCE - FUNCTIONAL EQUATIONS AND APPLICATIONS

Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics Classics in Applied Mathemat)

Stability of differential equations

Difference equations, stability theory and applications

Stability analysis of reaction–diffusion PDEs coupled at the boundaries with an ODE

Stability analysis for a class of functional differential equations and applications

Input-to-State Stability for PDEs

Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem

Stability of solutions for a heat equation with memory

Functional Equations

WITHDRAWN: Existence and stability for a heat equation with a non local boundary condition

Differential Equations Theory, Numerics and Applications

Lipschitz Stability for Backward Heat Equation with Application to Fluorescence Microscopy

Stability properties of a class kinetic equations including Boltzmann's equation

On the stability of a mixed type functional equation

A Stability Analysis of a Prototype Moving Boundary Problem in Heat Flow and Diffusion

Stability of the Drygas Functional Equation on Restricted Domain

ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

Geometric Theory of Semilinear Parabolic Equations

Optimal boundary control for the heat equation with application to freezing with phase change

The partial differential equation u<sub>t</sub> + uu<sub>x</sub> = μ<sub>xx</sub>

Existence of analytic solutions for the classical Stefan problem

Boundary Control of PDEs

On a quasi-linear parabolic equation occurring in aerodynamics

Input-to-state stability of infinite-dimensional control systems