Publikation: Instability of coupled systems with delay
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2012
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Communications on Pure & Applied Analysis. American Institute of Mathematical Sciences. 2012, 11(5), pp. 1753-1773. ISSN 1534-0392. eISSN 1553-5258. Available under: doi: 10.3934/cpaa.2012.11.1753
Zusammenfassung
We consider linear initial-boundary value problems that are a coupling like second-order thermoelasticity, or the thermoelastic plate equation or its generalization (the α-β-system introduced in [1, 26]). Now, there is a delay term given in part of the coupled system, and we demonstrate that the expected inherent damping will not prevent the system from not being stable; indeed, the systems will shown to be ill-posed: a sequence of bounded initial data may lead to exploding solutions (at any fixed time).
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510 Mathematik
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RACKE, Reinhard, 2012. Instability of coupled systems with delay. In: Communications on Pure & Applied Analysis. American Institute of Mathematical Sciences. 2012, 11(5), pp. 1753-1773. ISSN 1534-0392. eISSN 1553-5258. Available under: doi: 10.3934/cpaa.2012.11.1753BibTex
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year={2012},
doi={10.3934/cpaa.2012.11.1753},
title={Instability of coupled systems with delay},
number={5},
volume={11},
issn={1534-0392},
journal={Communications on Pure & Applied Analysis},
pages={1753--1773},
author={Racke, Reinhard}
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<dcterms:abstract xml:lang="eng">We consider linear initial-boundary value problems that are a coupling like second-order thermoelasticity, or the thermoelastic plate equation or its generalization (the α-β-system introduced in [1, 26]). Now, there is a delay term given in part of the coupled system, and we demonstrate that the expected inherent damping will not prevent the system from not being stable; indeed, the systems will shown to be ill-posed: a sequence of bounded initial data may lead to exploding solutions (at any fixed time).</dcterms:abstract>
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