Stability Indices for Nonlinear Waves and Patterns in Many Space Dimensions (18frg225)


(Memorial University of Newfoundland)

(Boston University)

(University of North Carolina at Chapel Hill)

(University of Missouri)


The Banff International Research Station will host the "Stability Indices for Nonlinear Waves and Patterns in Many Space Dimensions" workshop in Banff from June 17, 2018 to June 24, 2018.

An important goal when using mathematical equations to model physical systems is to be able to use those equations to predict observable, real-world behaviours. One key aspect of this is being able to identify important solutions to the equations, which represent corresponding structures in the physical system such as vortices in fluids and periodic patterns in chemical reactions, and determine their stability. Stable solutions tend to attract nearby initial data and are thus typically observable, whereas unstable solutions are repelling. Although the latter are not typically observable, they nevertheless provide information about the types of behaviours one can expect to observe.

Mathematically, it is well understood how to determine the stability of solutions to models with only one spatial dimension. However, most real-world systems occur in multiple spatial dimensions. There are very few techniques for determining stability in this case, and those techniques that do exist have proved to be of limited practical use. The goal of this focused research group is to develop a method for determining stability in multiple spatial dimensions that is applicable to models of real physical systems.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).