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Preservation of asymptotic behaviour in differential equations under deterministic or stochastic forcing

MACSI at the department of Mathematics and Statistics at the University of Limerick invites you to a seminar

Date: Friday,  15th  March 2019, Room A2-002 @ 15.00

Speaker: Prof. John Appleby, Department of Mathematical Sciences, Dublin City University

Title: Preservation of asymptotic behaviour in differential equations under deterministic or stochastic forcing 

Abstract: In this talk, we consider autonomous differential equations which have been subjected to forcing terms. The underlying asymptotic behaviour of the unforced system U is well-understood, but can be dramatic, as the equations considered are permitted to be highly nonlinear. Such asymptotic behaviour can include blow-up, finite-time convergence to an equilibrium, or very rapid growth or decay, of solutions. Different types of forcing terms are allowed, which can be deterministic, stochastic, state-dependent, or state-independent. 

The question the talk seeks to address is simply: what is the critical size of the forcing term below which the forced equation P retains an asymptotic property A of the unperturbed equation U, but above which the original asymptotic property A is destroyed? The property A is often a statement about precise growth or decay rates of solutions, or asymptotic estimates when approaching a  singularity. Therefore, we seek theorems which give necessary and sufficient conditions on the data of equation P for its solutions to inherit property A from U. 

Since proofs are generally technical and idiosyncratic to the class of forcing term, we merely give some ideas of the methods used, together with a survey of recent results. Some remarks concerning the extension of these results to functional differential equations, and to the recovery of the continuous-time results in numerical simulations, may also be germane. 

Further Information: If you have any questions regarding this seminar, please direct them to Romina Gaburro (061 2131930, email romina.gaburro@ul.ie  or Clifford Nolan (061 202766), clifford.nolan@ul.ie).

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.

 

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