Curriculum Vitae
Fei-Ran Tian

Personal

Citizenship: USA

Current Employment

Position: Professor
Address: Dept. of Mathematics, Ohio State Univ., 231 W. 18th Avenue, Columbus, OH 43210
Phone: 614-292-0852, FAX: 614-292-1479
E-mail: tian@math.ohio-state.edu

Education

• B.S. Mathematics, Jinan University, China, 1984
• M.S. Mathematics, Clarkson University, 1987
• Ph.D. Mathematics, Courant Institute, 1991
  Thesis: Oscillations of the Zero Dispersion Limit of the Korteweg-de Vries Equation
  Advisor: Peter D. Lax

Research Interests

• Partial Differential Equations and Analysis: integrable systems, zero dispersion or semi-classical limits, Whitham equations, modulation of dispersive oscillations.

Employment Record

• 9/91-8/93: The Dickson Instructor of Mathematics, University of Chicago
• 9/93-8/94: Postdoc, Mathematical Sciences Research Institute, Berkeley
• 9/94-8/95: Visiting Member, Courant Institute
• 9/95-8/02: Assistant Professor of Mathematics, The Ohio State University
• 9/02-8/09: Associate Professor of Mathematics, The Ohio State University
• 9/09-Now: Professor of Mathematics, The Ohio State University

Honors

• GSAS Dean's Dissertation Award, New York University, 1990.
• The Wilhelm T. Magnus Prize for Significant Contributions to Mathematical Sciences, Courant Institute, 1992.
• John Simon Guggenheim Fellow, 2003.
• Honorary Professorship, Huang-Gang Normal University, 2007.

Personal Grants and Contracts

• OSU Seed Grant-221770, Jan 1996 - Jun 1997.
• NSF grant DMS-9622810, Jul 1996 - Dec 1999.
• NSF grant DMS-0103849, Jun 2001 - Jun 2004.
• NSF grant DMS-0404931(with Y. Kodama), Jul 2004 - Dec 2007.

Publications

1. Oscillations of the Zero Dispersion Limit of the Korteweg-de Vries Equation, Comm. Pure Appl. Math. 46(1993), 1093-1129.
2. (with G.L. Vasconcelos) Rotation Invariance for Steady Hele-Shaw Flows, Phys. Fluid A 5(1993), 1863-1865.
3. On the Initial Value Problem of the Whitham Averaged System, in Singular Limits of Dispersive Waves, N. Ercolani, I. Gabitov, D. Levermore and D. Serre eds., NATO ARW series, Series B: Physics Vol.320, Plenum, New York (1994), 135-141.
4. The Initial Value Problem of the Whitham Averaged System, Comm. Math. Phys. 166(1994), 79-115.
5. The Whitham Type Equations and Linear Overdetermined Systems of Euler-Poisson-Darboux Type, Duke Math. Jour. 74(1994), 203-221.
6. On the Breakdown of Hele-Shaw Solutions with Non-zero Surface Tension, J. Nonlinear Sci. 5(1995), 479-484.
7. A Cauchy Integral Approach to Hele-Shaw Problems with a Free Boundary: The Zero Surface Tension Case, Arch. Rational Mech. Anal. 135(1996), 175-196.
8. (with M. Shelley, K. Wlodarski) Hele-Shaw Flows and Pattern Formation in a Time-Dependent Gap, Nonlinearity 10(1997), 1471-1495.
9. (with Q. Nie) Singularities in Hele-Shaw Flows, SIAM J. Appl. Math. 58(1998), 34-54.
10. (with J. Ye) On the Whitham Equations for the Semi-Classical Limit of the Defocusing Nonlinear Schr\"{o}dinger Equation, Comm. Pure Appl. Math. 52(1999), 655-692.
11. Hele-Shaw Problems in Multi-dimensional Spaces, J. Nonlinear Sci. 10 (2000), 275-290.
12. (with J. Ye) On the Breaking of the Single Phase Whitham Solution, Phys. Lett. A. 277(2000), 115-119.
13. (with Q. Nie) Singularities in Hele-Shaw Flows Driven by a Multipole, SIAM J. Appl. Math. 62(2001), 385-406.
14. (with H. Ceniceros) A Numerical Study of the Semi-Classical Limit of the Focusing Nonlinear Schr\"{o}dinger Equation, Phys. Lett. A, 306(2002), 25-34.
15. (with T. Grava) The Generation, Propagation and Extinction of Multiphases in the KdV Zero Dispersion Limit, Comm. Pure Appl. Math. 55(2002), 1569-1639.
16. On Hele-Shaw Flows with Anisotropic Surface Tension, Applied Math Lett. 16(2003), 715-721.
17. (with T. Grava) Large Parameter Behavior of Equilibrium Measure, Comm. Math. Sci. 4(2006), 551-573.
18. (with V. Pierce) Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations, Comm. Math. Sci. 4(2006), 799-822.
19. (with V. Pierce) Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation, Dynamics of PDE, 4(2007), 87-109.
20. (with V. Pierce) Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations for the KdV Hierarchy, Dynamics of PDE, 4(2007), 263-282.
21. (with Y. Kodama, V. Pierce) On the Whitham Equations for the Defocusing Complex Modified KdV Equation, SIAM J. Math Anal., 40(2008), 1750-1782.
22. (with T. Grava, V. Pierce) Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation, Physica D, 238(2009) 55-66.
23. Large Time Behavior of the Camassa-Holm Oscillations, in preparation.
24. On the Non-Strictly Whitham Equations for the Higher Order KdV Equations, in preparation.
25. On the Initial Value Problem of the Whitham Equations for the KdV Hierarchy, in preparation.

Invited Presentations

1. Initial Value Problem of the Whitham Equations, Colloquium, Duke University, February 1991.
2. On the Initial Value Problem of the Whitham Averaged System, NATO Workshop on "Singular Limits of Dispersive Waves", Lyon, France, July 1991.
3. The Initial Value Problem of the Whitham Averaged System, Potsdam-Kiev International Meeting, Potsdam, August 1991.
4. The Whitham Equations, Applied Math Seminar, University of Chicago, November 1991.
5. The Whitham Equations, NEEDS 1992, Dubna, Russia, July 1992.
6. The Macroscopic Structure of Nonlinear Dispersive Oscillations, Colloquium, Michigan State University, February 1993.
7. Hele-Shaw Flows, PDE Seminar, UC Berkeley, November 1993.
8. A Cauchy Integral Approach to Hele-Shaw Problem, MSRI Seminar, March 1994.
9. Hele-Shaw Flows, Colloquium, IUPUI, March 1994.
10. A Cauchy Integral Approach to Hele-Shaw Problem, Colloquium, SUNY at Buffalo, October 1994.
11. A Cauchy Integral Approach to Hele-Shaw Problem, Colloquium, Brown University, February 1995.
12. A Cauchy Integral Approach to Hele-Shaw Problem, Colloquium, Ohio State University, February 1995.
13. New Results on the Whitham Equations, Applied Math Seminar, Ohio State University, February 1995.
14. Hele-Shaw Flows, Colloquium, UC Santa Cruz, March 1995.
15. Lagrange Multipliers, Colloquium, UC Santa Cruz, March 1995.
16. New Results on Hele-Shaw Flows, Colloquium, UC Davis, March 1995.
17. Development of Singularities of Solutions of the Whitham Equations, the First Tianyan Conference on Mathematical Sciences, Berkeley, June 1997.
18. The Semi-classical Limit of the Focusing NLS Equation, Applied Math Seminar, Duke University, March 1998.
19. Some Computational Results on the Semi-classical Limit of the Focusing NLS, IMACS International Conference on "Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory", Athens, Georgia, April 1999.
20. New Results on the Focusing NLS, Applied Math Seminar, The Hong Kong University of Science and Technology, July 1999.
21. Hele-Shaw Flows, Workshop on "Modeling of Pattern Formation and Material Interfaces", Beijing International Center for Computational Physics, Beijing, China, July 1999.
22. The Whitham Equations, Applied Math Seminar, Qinghua University, Beijing, China, July 1999.
23. Singularities in Hele-Shaw Flows, Applied Math Seminar, Chinese University of Hong Kong, August 1999.
24. Hodograph Solutions of Whitham Type Equations, IMA workshop on "Dispersive Corrections to Transport Equations", May 2000.
25. An Example of a Double Phase in KdV-Whitham Equations, Workshop on "Whitham Equations and Their Applications in Mathematics and Physics", International School for Advanced Studies, Trieste, Italy, November 2000.
26. The Generation, Propagation and Extinction of Multiphases in the KdV Zero Dispersion Limit, AMS-IMS-SIAM Summer Research Conference on "The Legacy of the Inverse Scattering Transform in Nonlinear Wave Propagation", Mount Holyoke College, Massachusetts, June 2001.
27. The Generation, Propagation and Extinction of Multiphases in the KdV Zero Dispersion Limit, Conference on "Soliton Equations: Applications and Theory", University of Colorado at Colorado Springs, Colorado, August 2001.
28. The Interaction of Phases in KdV Modulations, Special Session on "Spectral Theory of Schr\"odinger Operators" in the 969th AMS Meeting, Columbus, Ohio, September 2001.
29. Phase Transition in KdV Oscillations, Dynamical Systems/Nonlinear Science Seminar, Princeton University, September 2001.
30. Lax-Levermore-Venakides Minimization Problem, Colloquium, Rensselaer Polytechnic Institute, September 2001.
31. Lax-Levermore-Venakides Minimization Problem, Analysis Seminar, Courant Institute, September 2001.
32. Phase Transition in KdV Oscillations, Applied Math Seminar, UC Irvine, October 2001.
33. Phase Transition in Dispersive Oscillations, Colloquium, Oklahoma State University, January 2002.
34. Phase Transition in Dispersive Oscillations, Colloquium, Southern Methodist University, February 2002.
35. Phase Transition in Dispersive Oscillations, Applied Math/PDE Seminar, University of Wisconsin at Madison, February 2002.
36. Phase Transition in Dispersive Oscillations, Colloquium, University of Texas at Arlington, February 2002.
37. Phase Transition in KdV Modulations, Special Session on "Partial Differential Equations" in 2002 AMS Central Section Meeting, Ann Arbor, Michigan, March 2002.
38. Phase Transition in Dispersive Oscillations, PDE and Applied Math Seminar, University of Maryland, March 2002.
39. New Results on the Zero Dispersion Limit of the KdV, Special Session on "Asymptotics of Integrable Partial Differential Equations, Riemann-Hilbert Problem and Related Topics" in the 982nd AMS Meeting, Orlando, Florida, November 2002.
40. Phase Transition in KdV Oscillations, Colloquium, Wright State University, January 2003.
41. Phase Transition in Dispersive Oscillations, Integrable Systems and Analysis Seminar, Duke University, February 2003.
42. Dispersive Oscillations: An Overview, IMS Lecture, Chinese University of Hong Kong, February 2004.
43. Phase Transition in Dispersive Oscillations, Applied Mathematics Seminar, Hong Kong University of Science and Technology, February 2004.
44. Dispersive Oscillations: A Minimization Problem, IMS Lecture, Chinese University of Hong Kong, February 2004.
45. New Results on Equilibrium Measure, Special Session on "Integrable Systems in Mathematics and Physics" in the 995th AMS meeting, Athens, Ohio, March 2004.
46. Phase Transition in Dispersive Oscillations, PDEs and Numerical Methods Seminar, Penn State University, April 2004.
47. Large Parameter Behavior of Equilibrium Measure, Geometry & Mathematical Physics Seminar, SISSA, Italy, June 2004.
48. On the Non-strictly Hyperbolic Whitham Equations, Minisymposiam on ``Zero Dispersion and Continuum Limits'' in SIAM Conference on Nonlinear Waves and Coherent Structure, Orlando, Florida, October 2004.
49. Zero Dispersion Limits, PDE Seminar, OSU, March 2005.
50. Zero Dispersion Limits, Colloquium, Zhongshan University, China, August 2005.
51. Large Time Behavior of the Zero Dispersion Limit of the KdV Hierarchy, Special Session on ``Integrable systems and the random matrix theory'' in the 23rd International Conference of Differential Geometric Methods in Theoretical Physics, Tianjin, China, August 2005.
52. Large Time Behavior of the Zero Dispersion Limit of the higher order KdV equation, Speciall session on ``PDEs and Geometric Analysis'' in AMS Spring Central Sectional Meeting, Notre Dame, IN, April 2006.
53. Large Time Behavior of the Zero Dispersion Limit of the higher order KdV equation, PDE Seminar, OSU, May 2006.
54. Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations, PDE Seminar, OSU, April 2007.
55. Non-Strictly Hyperbolic Whitham Equations, PDE Seminar, IMS, Chinese University of Hong Kong, June 2007.
56. Integrable Systems, Colloquium, Huang-Gang Normal University, June 2007.
57. Non-Strictly Hyperbolic Whitham Equations, Special Session on ``Integrable Equations, Their Special Limits and Riemann-Hilbert Approach'' in 32nd SIAM-SEAS 2008, Orlando, FL, March 2008.
58. Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation, Differential Equation Seminar, University of Michigan, March 2008.
59. Initial Value Problem of the Whitham Equations for the Canassa-Holm Equation, Colloquium, Georgetown University, March 2009.
60. Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation, Minisymposium on ``Asymptotic and Multiscale Analysis'' in SIAM Conference on Nonlinear Waves and Coherent Structures, Philadelphia, August 2010.
61. Initial Value Problem of the Modulation Equations for the Camassa-Holm equation Colloquium, Shanghai Jiaotong University, June 2011.
62. Weak Limits of Dispersive Oscillations and Their Dynamics, Colloquium, CMS, Zhejiang University, June 2011.
63. Weak Limits of Dispersive Oscillations and Their Dynamics, Colloquium, Zhongshan University, July 2011.

Other Visits

• Courant Institute, May 1992
• Courant Institute, September 1997
• Courant Institute, September 1998
• University of Maryland, October 1998
• IPAM of UCLA, April 2001
• Princeton University, September 2001
• University of Maryland, March 2002
• Courant Institute, September & October 2003
• IMS of CUHK, February 2004
• SISSA of Italy, May & June 2004
• Zhongshan University, China, August 2005
• IMS of CUHK, June 2007
• Shanghai Jiaotong University, June 2011

Other Activities

• Co-organizer of the session `Singular and Semiclassical Limits of Nonlinear Waves' in the first IMACS International Conference on "Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory", Athens, Georgia, April 1999.
• Member of Scientific Program Committee, the second IMACS International Conference on "Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory", Athens, Georgia, April 2001.
• Reviewer of grant proposals for U.S. Civilian Research and Development Foundation, 2001.
• Co-organizer (with Best, Guan, Lou, Terman) of the Conference in honor of Avner Friedman's 75th Birthday: ``Differential Equations and Math Biology'', Ohio State University, November 2007.
• Co-organizer (with Friedman, Guan, Kao and Lou) of the Conference ``Sixty-First Midwest PDE Seminar'', Ohio State University, November 2008.