Research Interests for Thomas P Witelski

My primary area of expertise is the solution of nonlinear ordinary and partial differential equations via perturbation methods. Using asymptotics along with a mixture of other applied mathematical techniques in analysis and scientific computing I study a broad range of applications in physical systems. Focuses of my work include problems in viscous fluid flow, industrial applications, flow in porous media, mathematical biology, and granular materials. Through my research I am working to extend the understanding of nonlinear diffusion processes in physical systems. Studying problems in a range of different fields has given me a unique opportunity to interact with a diverse set of collaborators and to transfer analytic techniques across the traditional boundaries that separate fields.

Areas of Interest:

Fluid dynamics
Partial differential equations
Asymptotics/Perturbation methods
Industrial and Applied mathematics

Recent Publications

1. M.B. Gratton and T.P. Witelski, Coarsening of dewetting thin films subject to gravity, Physical Review E, vol. 77 no. 016301 (2008), pp. 1--11 [e016301]
2. David G. Schaeffer, Michael Shearer and T.P. Witelski, Boundary-value problems for hyperbolic PDE related to steady granular flow, Mathematics and Mechanics of Solids, vol. 12 no. 6 (2007), pp. 665-699 (DOI: 10.1177/1081286506067325.)
3. R. Levy,M. Shearer and T.P. Witelski, Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves, European Journal of Applied Mathematics, vol. 18 no. 6 (2006), pp. 679--708
4. T.P. Witelski, R. Levy and M. Shearer, Growing surfactant waves in thin liquid films driven by gravity, Applied Mathematics Research Express, vol. 2006 no. 15487 (2006), pp. 1-21
5. Mark Bowen and Thomas P. Witelski, The linear limit of the dipole problem for the thin film equation, SIAM journal on applied mathematics, vol. 66 no. 5 (2006), pp. 1727--1748