Research Interests

My background is in PDE and functional analysis with applications to invariant manifolds. My research addresses stability, bifurcation, and slow evolution of coherent structures in PDEs describing the evolution of nonlinear waves and gradient flows in polymer materials. Currently I study the development of pore networks in amphiphilic polymer materials used in energy conversion devices such as fuel cells, Lithium ion batteries, and polymer solar cells. 

Selected Publications

• K. Promislow and Qiliang Wu, Existence of pearled patterns in the planar Functionalized Cahn-Hilliard equation, Journal of Differential Equations, to appear  Open
• Juliana Duncan, Qiliang Wu, Keith Promislow, Graham Henkelman, Biased gradient-squared descent saddle point finding method, Journal of Chemical Physics, 140, 194102, http://dx.doi.org/10.1063/1.4875477 (2014).   Open
• Shibin Dai and Keith Promislow, Geometric Evolution of Bilayers under the Functionalized Cahn-Hilliard equation, Proceedings of the Royal Society London, Series A, 469 20120505 (2013).  Open
• Tom Bellsky, Arjen Doelman, Tasso Kaper, Keith Promislow, Adiabatic Stability of Semi-Strong Interactions in an Activator-Inhibitor system: The Weakly Damped Regime, Indiana University Math Journal 62, 1809–1859 (2013).   Open
• Todd Kapitula and Keith Promislow, Stability indices for constrained self-adjoint operators, Proceedings of the AMS, 140 (2012) 865-880.  Open