Group Activities :

Our research group in analytical and numerical analysis of evolution equations, modeling and computations focus on a broad range of nonlinear partial and ordinary differential equations that arise in physical and engineering applications. The analysis of these equations lies on the current frontier of mathematical and computational research, and it also plays an important role in the numerous areas of physics, engineering, and in the high technology sector.

Mary Pugh (associate professor University of Toronto), Almut Burchard (professor University of Toronto), Catherine Sulem (professor University of Toronto),
Gideon Simpson (postdoc University of Toronto), Benjamin Stephens (postdoc University of Washington), Marina Chugunova (postdoc University of Toronto).

Collaborators:

Roman Taranets (professor Institute of Applied Mathematics and Mechanics NAS of Ukraine), Eugene Benilov, (professor University of Limerick),
Pyatkov Sergey (professor Sobolev Institute of Mathematics), Pelinovsky Dmitry (associate professor McMaster University)

Meeting dates and talks:
(Location: 10th floor Huron 215; Time: 5pm - 6pm on Wednesdays)

39. group meeting ( December 1, 2010)
"Gradient flow approach to linearizations of thin-film equations II."

38. group meeting ( November 24, 2010)
"Gradient flow approach to linearizations of thin-film equations I."

37. meeting with Dejan Slepcev ( November 18, 2010)
"Generalized gradient flow and long-wave unstable thin-film equations."

36. group meeting ( November 10, 2010)
"Existence and non-existence of self-similar solutions of a thin-film equation."

35. group meeting ( November 3, 2010)
"Recent uniqueness results."

34. Gideon Simpson ( October 13, 2010)
"Coherent Structures in the Nonlinear Maxwell Equations"

33. Dan Ginsberg ( October 6, 2010, 5-6 pm)
"Uniform positivity result for weak steady states in coating flows."

32. Marina Chugunova ( September 29, 2010, 5-6 pm)
"Thin film equations: uniqueness and non-uniqueness results."

31. Almut Burchard ( September 22, 2010, 5-6 pm)
"Global behavior of strong solutions in a coating flow model."

30. Mark Fortier ( TBA)
"Almost Sure Convergence of Rearrangements."

29. Lev Sakhnovich ( May 25, 2010)
"Extremal non-negative trigonometrical and power polynomials of several variables."

28. Robert McCann ( April 7, 2010)
"Introduction to steepest descent in the Wasserstein metric."

27. Al Stauffer (York University) ( March 24, 2010)
"Solving the Schroedinger Equation for scattering states: Dealing efficiently and accurately with large radial values."

26. Marina Chugunova ( March 17, 2010)
"On spectral parameter dependent boundary conditions."

25. Ian Zwiers ( March 10, 2010)
"Computing Negative Eigenvalues for a Schrodinger Operator with Non-Diagonal Potential. Both how and why."

24. Anton Sakovich (McMaster University) ( March 3, 2010)
"Global well-posedness of the short-pulse and sine-Gordon equations in energy space."

23. Damir Kinzebulatov ( February 3, 2010)
"Sobolev-type inequalities on singular sets."

22. Gideon Simpson ( January 27, 2010)
"A Quantum Correction to the Zakharov Equations."

21. Almut Burchard ( January 20, 2010)
"On the rate of convergence to a steady state on the boundary for some thin film equation."

20. Chugunova Marina ( December 16, 2009)
"Numerical computations and stability of solitons for some thin-film equation."

19. Joel Phillips ( December 9, 2009)
"Quadrature rules for high-order finite element method."

18. Xiao Liu ( December 2, 2009)
"Numerical simulation of resonant tunneling for nonlinear cubic Schrodinger equation."

17. William Bordeaux Montrieux ( November 18, 2009)
"Random perturbations of spectrum of non-selfadjoint differential operators."

16. Chugunova Marina ( November 4, 2009)
"Stampacchia’s iteration lemma and speed of propagation of the interface for the thin film equations II."

15. Working meeting ( October 28, 2009)
"Short 15 min. presentations of recent results"

14. Chugunova Marina ( October 14, 2009)
"Stampacchia’s iteration lemma and speed of propagation of the interface for the thin film equations I."

13. Gideon Simpson ( October 7, 2009)
"Is there anybody in there? Ruling out embedded eigenvalues of some linearized NLS operators. "

12. Roman Taranets (July 31, 2009)
"Complex valued solutions for a thin film equation."

11. Benjamin Stephens (July 24, 2009)
"Wasserstein metric approach to some thin film problem."

10. Almut Burchard (July 22, 2009)
"On symmetrical rearrangement approach to a thin film problem."

9. Benjamin Stephens (April 1, 2009)
"Linear stability near self-similarity in a fourth-order evolution."

8. Gideon Simpson (March 4, 2009)
"Nonlinear geometrical optics applied to low contrast optical media."

7. Benjamin Stephens (January 28, 2009)
" Slicing convex bodies and the geodesic Radon transform."

6. Marina Chugunova (January 14, 2009)
"Traps and counterexamples in numerical approximations of eigenvalues of unbounded self-adjoint operators by eigenvalues of finite matrices."

5. Gideon Simpson (December 3, 2008)
"On homogenization of complex fluids. (work in progress) "

4. Benjamin Stephens (November 12, 2008)
" Evolution equations. Introduction to Wasserstein metric approach."

4. Benjamin Stephens (November 12, 2008)
" Evolution equations. Introduction to Wasserstein metric approach."

3 Marina Chugunova (October 29, 2008)
" On existence of positive periodic steady states in some thin film evolution equation. (work in progress) "

2. Mary Pugh (October 15, 2008)
" Some numerical approach to a non-linear evolution equation arising in rimming flow dynamic "

1. Gideon Simpson ( October 1, 2008)
" A novel spectral method for computing high quality representations of solitary wave solutions to nonlinear wave equations. (work in progress) "