Stability of Multidimensional Waves (19rit022)


(College of Charleston)

(Miami University)


The Banff International Research Station will host the "Stability of multidimensional waves" workshop in Banff from June 2, 2019 to June 9, 2019.

This proposal deals with the concept of stability. Stability is a fun- damental concept in physics. An illustration of this concept is given by trying to make a pencil stand on its lead. In theory, it is possi- ble but, in practice, because it is such an unstable state, it cannot be done. In the example just described, the study of stability is very simple and there is no need for a mathematical analysis to prove or disprove the stability of the system. The concept of stability carries over to solutions of differential equations such as the ones forming the combustion models mentioned above. In this context, the concept of stability takes an abstract form and its study often involves some so- phisticated mathematical tools. However, such a study is fundamental because only stable solutions can be seen experimentally, i.e. seen in a real-life event. Unstable solutions, just like in the case of the pencil explained above, although exist in theory will never be observed.

The goal of the project is to study stability of certain special solutions to systems of partial differential equations posed on multidimensional domains. These system of equations serve as mathematical models for natural phenomena or experiments. For example, one of the models we our analysis will be applicable to deals with the phenomenon of gas combustion in a porous medium.

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).