Thomas P. Witelski

Thomas P. Witelski
  • Professor in the Department of Mathematics
  • Professor in the Department of Mechanical Engineering and Materials Science (Secondary)
External address: 295 Physics Bldg, Box 90320, Durham, NC 27708-0320
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2841

Research Areas and Keywords


perturbation methods

Computational Mathematics

numerical partial differential equations

PDE & Dynamical Systems

fluid dynamics, nonlinear partial differential equations, dynamical systems, perturbation methods

Physical Modeling

fluid dynamics

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.

Education & Training
  • Ph.D., California Institute of Technology 1995

  • B.S.E., The Cooper Union 1991

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

Witelski, T. P. “Shocks in nonlinear diffusion.” Applied Mathematics Letters, vol. 8, no. 5, Jan. 1995, pp. 27–32. Scopus, doi:10.1016/0893-9659(95)00062-U. Full Text

Witelski, T. P. “Merging traveling waves for the porous-Fisher's equation.” Applied Mathematics Letters, vol. 8, no. 4, Jan. 1995, pp. 57–62. Scopus, doi:10.1016/0893-9659(95)00047-T. Full Text

Cohen, D. S., et al. “Shock formation in a multidimensional viscoelastic diffusive system.” Siam Journal on Applied Mathematics, vol. 55, no. 2, Jan. 1995, pp. 348–68. Scopus, doi:10.1137/S0036139993269333. Full Text

Witelski, T. P. “An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation.” Journal of Mathematical Biology, vol. 33, no. 1, Nov. 1994, pp. 1–16. Scopus, doi:10.1007/BF00160171. Full Text

Witelski, T., et al. “An application of pattern recognition and infrared spectroscopy to water analysis.” International Journal of Environmental Analytical Chemistry, vol. 44, no. 2, May 1991, pp. 127–36. Scopus, doi:10.1080/03067319108027542. Full Text

Witelski, Thomas, and Mark Bowen. “Singular perturbation theory.” Scholarpedia, vol. 4, no. 4, Scholarpedia, pp. 3951–3951. Crossref, doi:10.4249/scholarpedia.3951. Full Text

JI, H. A. N. G. J. I. E., and THOMAS P. WITELSKI. “Steady states and dynamics of a thin-film-type equation with non-conserved mass.” European Journal of Applied Mathematics, Cambridge University Press (CUP), pp. 1–34. Crossref, doi:10.1017/s0956792519000330. Full Text