Explosions and explosion control in deterministic and stochastic differential equations

Jan 9, 2020
3:15 PM - 4:15 PM
Prof. Dr. John Appleby
Dublin City University, School of Mathematical Sciences
TUD Mathematik Oberseminar Analysis
Main Topic
Prof. Dr. S. Siegmund
In this talk, we give a survey of our recent results which characterise whether solutions of autonomous scalar functional differential equations can be continued for all time, or have a finite interval of existence. In the case that the interval of existence is finite, the solution often "explodes", or tends to infinity as the end of the interval is approached. While we do not consider particular applications, we note that such behaviour can be undesirable in real-world systems, and therefore ask whether by applying appropriate controls, the blow-up, non-continuability, or rapid growth, of solutions can be tempered. Part of the talk is therefore devoted to determining sharp conditions on control terms, which can be delayed or instantaneous, which prevent these types of unbounded behaviour. This leads us to consider certain special classes of differential equations with state-dependent delay. As a simple case study, we examine scalar equations in which the control can be achieved by using observations at fixed instants in time, and in which the delayed, controlling, force is piecewise constant. Time permitting, we will consider some results for stochastic systems also. Our philosophy throughout is to consider relatively simple equations, but to try to obtain necessary and sufficient conditions on control forces and (state-dependent) delays which achieve the appropriate control.
Parts of the work presented are joint with Denis Patterson (Brandeis, Boston) and Xuerong Mao (Strathclyde, Glasgow).

Last modified: Nov 19, 2019, 3:19:16 PM


TUD Willers-Bau (WIL C 129)Zellescher Weg12-1401069Dresden


TUD MathematikWillersbau, Zellescher Weg12-1401069Dresden
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