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Research Interests for Thomas P. Witelski

Research Interests: Fluid Dynamics, Perturbation Methods, Asymptotic Analysis, Nonlinear Ordinary and Partial differential equations

My primary area of expertise is the solution of nonlinear ordinary and partial differential equations via perturbation methods. Using asymptotics along with a mixture of other applied mathematical techniques in analysis and scientific computing I study a broad range of applications in physical systems. Focuses of my work include problems in viscous fluid flow, dynamical systems, and industrial applications. Through my research I am working to extend the understanding of nonlinear diffusion processes in physical systems. Studying problems in a range of different fields has given me a unique opportunity to interact with a diverse set of collaborators and to transfer analytic techniques across the traditional boundaries that separate fields.

Keywords:
Differential equations, Nonlinear, Differential equations, Parabolic, Fluid dynamics, Perturbations, asymptotics, Surface Tension
Areas of Interest:

Fluid dynamics
Partial differential equations
Asymptotics/Perturbation methods
Industrial and Applied mathematics

Recent Publications   (search)
  1. Aguareles, M; Chapman, SJ; Witelski, T, Dynamics of spiral waves in the complex Ginzburg–Landau equation in bounded domains, Physica D: Nonlinear Phenomena, vol. 414 (December, 2020) [doi[abs]
  2. JI, H; WITELSKI, TP, Steady states and dynamics of a thin-film-type equation with non-conserved mass, European Journal of Applied Mathematics, vol. 31 no. 6 (December, 2020), pp. 968-1001, Cambridge University Press (CUP) [doi[abs]
  3. Dijksman, JA; Mukhopadhyay, S; Gaebler, C; Witelski, TP; Behringer, RP, Erratum: Obtaining self-similar scalings in focusing flows [Phys. Rev. E 92, 043016 (2015)]., Physical Review. E, vol. 101 no. 5-2 (May, 2020), pp. 059902 [doi[abs]
  4. Witelski, TP, Nonlinear dynamics of dewetting thin films, Aims Mathematics, vol. 5 no. 5 (January, 2020), pp. 4229-4259 [doi[abs]
  5. Dijksman, JA; Mukhopadhyay, S; Behringer, RP; Witelski, TP, Thermal Marangoni-driven dynamics of spinning liquid films, Physical Review Fluids, vol. 4 no. 8 (August, 2019) [doi[abs]

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320