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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.

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

Representative Publications   (search)
  1. Witelski, T; Bowen, M, Methods of Mathematical Modelling: Continuous Systems and Differential Equations (September, 2015), pp. 1-305, Springer International Publishing, ISBN 9783319230412 [doi[abs] [author's comments]
  2. Ji, H; Witelski, T, 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. Liu, W; Witelski, TP, Steady states of thin film droplets on chemically heterogeneous substrates, Ima Journal of Applied Mathematics, vol. 85 no. 6 (November, 2020), pp. 980-1020, Oxford University Press (OUP) [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]
  6. Bowen, M; Witelski, TP, Pressure-dipole solutions of the thin-film equation, European Journal of Applied Mathematics, vol. 30 no. 2 (April, 2019), pp. 358-399 [doi[abs]
  7. Gao, Y; Ji, H; Liu, JG; Witelski, TP, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete and Continuous Dynamical Systems Series B, vol. 23 no. 10 (December, 2018), pp. 4433-4453, American Institute of Mathematical Sciences (AIMS) [doi[abs]
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Mathematics Department
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