Professor in the Department of Mathematics
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.
Appointments and Affiliations
- Professor in the Department of Mathematics
- Professor in the Thomas Lord Department of Mechanical Engineering and Materials Science
- Professor in the Department of Mechanical Engineering and Materials Science
Contact Information
- Office Location: 120 Science Drive, Durham, NC 27708-0320
- Email Address: witelski@duke.edu
- Websites:
Education
- B.S.E. The Cooper Union, 1991
- Ph.D. California Institute of Technology, 1995
Awards, Honors, and Distinctions
- Top 5% teaching. Duke Arts and Science. 2018
- Top 5% teaching. Duke Arts and Science. 2017
- Faculty Early Career Development (CAREER) Program. National Science Foundation. 2003
- Sloan Research Fellowship-Mathematics. Alfred P. Sloan Foundation. 2000
Courses Taught
- MATH 895: Internship
- MATH 790-90: Minicourse in Advanced Topics
- MATH 577: Mathematical Modeling
- MATH 553: Asymptotic and Perturbation Methods
- MATH 551: Applied Partial Differential Equations and Complex Variables
Representative Publications
- Bowen, M., J. R. King, and T. P. Witelski. “CAUCHY-DIRICHLET PROBLEMS FOR THE POROUS MEDIUM EQUATION.” Discrete and Continuous Dynamical Systems- Series A 43, no. 3–4 (March 1, 2023): 1143–74. https://doi.org/10.3934/dcds.2022182.
- Bowen, M., and T. P. Witelski. “Pressure-dipole solutions of the thin-film equation.” European Journal of Applied Mathematics 30, no. 2 (April 1, 2019): 358–99. https://doi.org/10.1017/S095679251800013X.
- Ji, H., and T. P. Witelski. “Instability and dynamics of volatile thin films.” Physical Review Fluids 3, no. 2 (February 1, 2018). https://doi.org/10.1103/PhysRevFluids.3.024001.
- Witelski, T., and M. Bowen. Methods of Mathematical Modelling: Continuous Systems and Differential Equations, 2015. https://doi.org/10.1007/978-3-319-23042-9.
- Chapman, S Jonathan, Philippe H. Trinh, and Thomas P. Witelski. “Exponential Asymptotics for Thin Film Rupture.” SIAM J. Appl. Math. 73 (2013): 232–53. https://doi.org/10.1137/120872012.