报告人：Prof John Appleby, Dublin City University
题目：Blow-up, rapid growth and asymptotic behaviour in nonlinear differential systems: stochastic equations and numerical methods
摘要：The talk gives a snapshot of recent results under which diverse types of highly nonlinear differential equations possess solutions which exhibit convergence to equilibrium, unbounded growth, or finite--time convergence or blow-up. One goal is to determine sharp conditions on stochastic terms under which there are important quantitative or qualitative changes in asymptotic behaviour. Another goal is to develop efficient and computationally tractable numerical methods which preserve these qualitative and asymptotic properties, especially for stochastic differential equations.