Thomas P. Witelski
- Professor in the Department of Mathematics
- Professor in the Department of Mechanical Engineering and Materials Science (Secondary)
Research Areas and Keywords
numerical partial differential equations
PDE & Dynamical Systems
fluid dynamics, nonlinear partial differential equations, dynamical systems, perturbation methods
My primary area of expertise is the solution of nonlinear ordinary and partial differential equations for models of physical systems. Using asymptotics along with a mixture of other applied mathematical techniques in analysis and scientific computing I study a broad range of applications in engineering and applied science. Focuses of my work include problems in viscous fluid flow, dynamical systems, and industrial applications. Approaches for mathematical modelling to formulate reduced systems of mathematical equations corresponding to the physical problems is another significant component of my work.
DiCarlo, D. A., et al. “Nonmonotonic traveling wave solutions of infiltration into porous media.” Water Resources Research, vol. 44, no. 2, Feb. 2008. Scopus, doi:10.1029/2007WR005975. Full Text
Gratton, M. B., and T. P. Witelski. “Coarsening of unstable thin films subject to gravity.” Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 77, no. 1 Pt 2, Jan. 2008, p. 016301. Epmc, doi:10.1103/physreve.77.016301. Full Text
Gratton, M. B., and T. P. Witelski. “Coarsening of dewetting thin films subject to gravity.” Physical Review E, vol. 77, no. 016301, 2008, pp. 1–11.
Aguareles, M., et al. “Interaction of spiral waves in the Complex Ginzburg-Landau equation.” Physical Review Letters, vol. 101, no. 224101, 2008.
Schaeffer, D. G., et al. “Boundary-value problems for hyperbolic equations related to steady granular flow.” Mathematics and Mechanics of Solids, vol. 12, no. 6, Dec. 2007, pp. 665–99. Scopus, doi:10.1177/1081286506067325. Full Text
Levy, R., et al. “Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves.” European Journal of Applied Mathematics, vol. 18, no. 6, Dec. 2007, pp. 679–708. Scopus, doi:10.1017/S0956792507007218. Full Text
Witelski, T. P., et al. “Growing surfactant waves in thin liquid films driven by gravity.” Applied Mathematics Research Express, vol. 2006, Dec. 2006. Scopus, doi:10.1155/AMRX/2006/15487. Full Text
Bowen, M., and T. P. Witelski. “The linear limit of the dipole problem for the thin film equation.” Siam Journal on Applied Mathematics, vol. 66, no. 5, Oct. 2006, pp. 1727–48. Scopus, doi:10.1137/050637832. Full Text
Witelski, T. P., and S. W. Rienstra. “Introduction to practical asymptotics III.” Journal of Engineering Mathematics, vol. 53, no. 3–4, Dec. 2005, p. 199. Scopus, doi:10.1007/s10665-005-9027-9. Full Text
Münch, A., et al. “Lubrication models with small to large slip lengths.” Journal of Engineering Mathematics, vol. 53, no. 3–4, Dec. 2005, pp. 359–83. Scopus, doi:10.1007/s10665-005-9020-3. Full Text