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
Links

Research Areas and Keywords

Analysis

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., Cooper Union 1991

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

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