Thomas P. Witelski
- Professor in the Department of Mathematics
- Professor in the Department of Mechanical Engineering and Materials Science (Secondary)
Research Areas and Keywords
Analysis
Computational Mathematics
PDE & Dynamical Systems
Physical Modeling
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.
Witelski, T. P., and A. J. Bernoff. “Self-similar asymptotics for linear and nonlinear diffusion equations.” Studies in Applied Mathematics, vol. 100, no. 2, Jan. 1998, pp. 153–93. Scopus, doi:10.1111/1467-9590.00074. Full Text
Witelski, T. P. “Similarity solutions of the lubrication equation.” Applied Mathematics Letters, vol. 10, no. 5, Sept. 1997, pp. 107–13. Scopus, doi:10.1016/S0893-9659(97)00092-X. Full Text
Witelski, TP. "Perturbation Analysis for Wetting Fronts in Richards' Equation." Transport in Porous Media 27.2 (January 1, 1997): 121-134. Full Text
Witelski, T. P. “Segregation and mixing in degenerate diffusion in population dynamics.” Journal of Mathematical Biology, vol. 35, no. 6, Jan. 1997, pp. 695–712. Scopus, doi:10.1007/s002850050072. Full Text
Witelski, T. P. “Traveling wave solutions for case II diffusion in polymers.” Journal of Polymer Science, Part B: Polymer Physics, vol. 34, no. 1, Jan. 1996, pp. 141–50. Scopus, doi:10.1002/(SICI)1099-0488(19960115)34:1<141::AID-POLB12>3.0.CO;2-E. Full Text
Cohen, D. S., and T. P. Witelski. “Inaccessible states in time-dependent reaction diffusion.” Studies in Applied Mathematics, vol. 97, no. 4, Jan. 1996, pp. 301–19. Scopus, doi:10.1002/sapm1996974301. Full Text
Witelski, T. P. “The structure of internal layers for unstable nonlinear diffusion equations.” Studies in Applied Mathematics, vol. 97, no. 3, Jan. 1996, pp. 277–300. Scopus, doi:10.1002/sapm1996973277. Full Text
Witelski, T. P. “Stopping and merging problems for the porous media equation.” Ima Journal of Applied Mathematics (Institute of Mathematics and Its Applications), vol. 54, no. 3, Dec. 1995, pp. 227–43. Scopus, doi:10.1093/imamat/54.3.227. Full Text
Witelski, T. P., and D. S. Cohen. “Perturbed reversible systems.” Physics Letters A, vol. 207, no. 1–2, Oct. 1995, pp. 83–86. Scopus, doi:10.1016/0375-9601(95)00662-M. Full Text
Witelski, T. P., and D. S. Cohen. “Forbidden Regions for Shock Formation in Diffusive Systems.” Studies in Applied Mathematics, vol. 95, no. 3, Oct. 1995, pp. 297–317. Scopus, doi:10.1002/sapm1995953297. Full Text