Watershed initial conditions for propagating waves in a system with bistability: A weight-function approach. (May 2019)

• Record Type: Journal Article
• Authors: Watt, S.D.; Sidhu, H.S.; Jovanoski, Z.; Towers, I.N.; Huang, Z.
• Is Part Of: Applied mathematics letters. Volume 91(2019)
• Page Start: 106
• Page End: 112
• Publication Date: 2019-05
• Subjects: Bistability -- Critical initial conditions -- Travelling waves; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.11.018
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We consider non-adiabatic combustion waves arising from a two-step exothermic system. Our previous work showed that in certain parameter regions, the combustion wave can evolve to the "fast" solution branch, the "slow" solution branch or diffuse to the ambient temperature (extinction wave). Here, we are interested to find critical initial temperature profiles which evolve to these three types of steady solutions. For a particular family of temperature profiles, we construct a weight function which can be used to predict which of these three types of waves an initial temperature profile will evolve to.