On the response of physical systems governed by non-linear ordinary differential equations to step input

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10332644" target="_blank" >RIV/00216208:11320/16:10332644 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ijnonlinmec.2015.10.013" target="_blank" >http://dx.doi.org/10.1016/j.ijnonlinmec.2015.10.013</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ijnonlinmec.2015.10.013" target="_blank" >10.1016/j.ijnonlinmec.2015.10.013</a>

Result language
angličtina
Original language name
On the response of physical systems governed by non-linear ordinary differential equations to step input
Original language description
The response of physical systems governed by linear ordinary differential equations to step input is traditionally investigated using the classical theory of distributions. The response of non-linear systems is however beyond the reach of the classical theory. The reason is that the simplest non-linear operation multiplication is not defined for distributions. Yet the response of non-linear systems is of interest in many applications, and a framework capable of handling such problems is needed. We argue that a suitable framework is provided by Colombeau algebra that gives one the possibility to overcome the limitations of the classical theory of distributions, namely the possibility to simultaneously handle discontinuity, differentiation and non-linearity. Our thesis is documented by means of studying the response of two systems governed by non-linear ordinary differential equations subject to step input. In particular, we show that using the rules of calculus in Colombeau algebra it is possible to obtain an explicit and practically relevant characterisation of the behaviour of the considered systems at the point of the jump discontinuity.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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