
Thomas P. Witelski, Professor 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.
 Contact Info:
 Office Hours:
 Please email me to request a meeting time
 Education:
Ph.D.  California Institute of Technology  1995 
B.S.E.  The Cooper Union  1991 
 Specialties:

Applied Math
Applied Math
 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, industrial applications, flow in porous media, mathematical
biology, and granular materials. 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.
 Areas of Interest:
Fluid dynamics Partial differential equations Asymptotics/Perturbation methods Industrial and Applied mathematics
 Keywords:
Differential equations, Nonlinear • Differential equations, Parabolic • Fluid dynamics • Perturbations, asymptotics • Surface Tension
 Current Ph.D. Students
(Former Students)
 Postdocs Mentored
 Jeffrey Wong (September, 2017  2021)
 Saulo Orizaga (September, 2017  June, 2020)
 Rachel Levy (July, 2005  June, 2007)
 Anne Catlla (2005  2008)
 Anand Jayaraman (September 1, 2004  August 15, 2005)
 Sandra Wieland (January 1, 2004  December, 2004)
 Linda Smolka (April 8, 2002  July 1, 2004)
 Karl Glasner (2001/122002/05)
 Mark Bowen (2000/032001/12)
 Undergraduate Research Supervised
 Veronica Ciocanel (May, 2010  May, 2012)
Honorable mention for 2012 Faculty Scholar, Thesis: Modeling and numerical simulation of the nonlinear dynamics of the forced planar string pendulum  Jeremy Semko (May, 2009  May, 2010)
Thesis: Statistical Analysis of Simulations of Coarsening Droplets Coating a Hydrophobic Surface  Lingren Zhang (July, 2006  September, 2006)
Thesis: The Motion of Sets of Vortices Undergraduate summer research  Qinzheng Tian (July, 2005  September, 2005)
Thesis: Simulation of Newtonian fluid fluid between rotating cylinders Undergraduate summer research
 Representative Publications
(More Publications)
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 Witelski, T; Bowen, M, Methods of Mathematical Modelling: Continuous Systems and Differential Equations
(September, 2015),
pp. 1305, Springer International Publishing, ISBN 9783319230412 [doi] [abs] [author's comments]
 Ji, H; Witelski, T, Steady states and dynamics of a thinfilmtype equation with nonconserved mass,
European Journal of Applied Mathematics, vol. 31 no. 6
(December, 2020),
pp. 9681001, Cambridge University Press (CUP) [doi] [abs]
 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. 9801020, Oxford University Press (OUP) [doi] [abs]
 Witelski, TP, Nonlinear dynamics of dewetting thin films,
Aims Mathematics, vol. 5 no. 5
(January, 2020),
pp. 42294259 [doi] [abs]
 Dijksman, JA; Mukhopadhyay, S; Behringer, RP; Witelski, TP, Thermal Marangonidriven dynamics of spinning liquid films,
Physical Review Fluids, vol. 4 no. 8
(August, 2019) [doi] [abs]
 Bowen, M; Witelski, TP, Pressuredipole solutions of the thinfilm equation,
European Journal of Applied Mathematics, vol. 30 no. 2
(April, 2019),
pp. 358399 [doi] [abs]
 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. 44334453, American Institute of Mathematical Sciences (AIMS) [doi] [abs]
Journal editorial boards
Other Activities
