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Speaker(s): Marek Kryspin
Affiliation: Politechnika Wrocławska
Language of the talk: English
Date: Oct. 16, 2024, 2:15 p.m.
Room: room 5070
Seminar: Seminar of Biomathematics and Game Theory Group

The talk will present results concerning non-autonomous linear ODEs with delay (defined by an integral with respect to time-varying measures). In addition to standard results on the existence and uniqueness of solutions for such equations, new theorems addressing the continuous dependence of solutions on parameters (measures) will also be discussed.

For this purpose, facts ensuring the continuous dependence of the fixed point of a family of contractive mappings on the parameter will be used.
Moreover, a theorem will be discussed that allows replacing a delay differential equation with an equation involving a certain linear functional (defined by a single measure). This topic is related to measure integration and disintegration, and in the future, it may enable more precise studies on the continuous dependence of solutions on measures.
The results presented at the seminar, although discussed for scalar equations, can be extended to systems of ordinary differential equations with delay. Such systems are an important tool in mathematical ecology theory and are used to model interspecies relationships.

ODEs with general delay. Continuous dependence on measures

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