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
- Oscillations of the Zero Dispersion Limit of the Korteweg-de Vries Equation, Comm. Pure Appl. Math. 46(1993), 1093-1129.
- (with G.L. Vasconcelos) Rotation Invariance for Steady Hele-Shaw Flows, Phys. Fluid A 5(1993), 1863-1865.
- 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.
- The Initial Value Problem of the Whitham Averaged System, Comm. Math. Phys. 166(1994), 79-115.
- The Whitham Type Equations and Linear Overdetermined Systems of Euler-Poisson-Darboux Type, Duke Math. Jour. 74(1994), 203-221.
- On the Breakdown of Hele-Shaw Solutions with Non-zero Surface Tension, J. Nonlinear Sci. 5(1995), 479-484.
- 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.
- (with M. Shelley, K. Wlodarski) Hele-Shaw Flows and Pattern Formation in a Time-Dependent Gap, Nonlinearity 10(1997), 1471-1495.
- (with Q. Nie) Singularities in Hele-Shaw Flows, SIAM J. Appl. Math. 58(1998), 34-54.
- (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.
- Hele-Shaw Problems in Multi-dimensional Spaces, J. Nonlinear Sci. 10 (2000), 275-290.
- (with J. Ye) On the Breaking of the Single Phase Whitham Solution, Phys. Lett. A. 277(2000), 115-119.
- (with Q. Nie) Singularities in Hele-Shaw Flows Driven by a Multipole, SIAM J. Appl. Math. 62(2001), 385-406.
- (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.
- (with T. Grava) The Generation, Propagation and Extinction of Multiphases in the KdV Zero Dispersion Limit, Comm. Pure Appl. Math. 55(2002), 1569-1639.
- On Hele-Shaw Flows with Anisotropic Surface Tension, Applied Math Lett. 16(2003), 715-721.
- (with T. Grava) Large Parameter Behavior of Equilibrium Measure, Comm. Math. Sci. 4(2006), 551-573.
- (with V. Pierce) Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations, Comm. Math. Sci. 4(2006), 799-822.
- (with V. Pierce) Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation, Dynamics of PDE, 4(2007), 87-109.
- (with V. Pierce) Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations for the KdV Hierarchy, Dynamics of PDE, 4(2007), 263-282.
- (with Y. Kodama, V. Pierce) On the Whitham Equations for the Defocusing Complex Modified KdV Equation, SIAM J. Math Anal., 40(2008), 1750-1782.
- (with T. Grava, V. Pierce) Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation, Physica D, 238(2009) 55-66.
- Large Time Behavior of the Camassa-Holm Oscillations, in preparation.
- On the Non-Strictly Whitham Equations for the Higher Order KdV Equations, in preparation.
- On the Initial Value Problem of the Whitham Equations for the KdV Hierarchy, in preparation.
Invited Presentations
- Initial Value Problem of the Whitham Equations, Colloquium, Duke University, February 1991.
- On the Initial Value Problem of the Whitham Averaged System, NATO Workshop on "Singular Limits of Dispersive Waves", Lyon, France, July 1991.
- The Initial Value Problem of the Whitham Averaged System, Potsdam-Kiev International Meeting, Potsdam, August 1991.
- The Whitham Equations, Applied Math Seminar, University of Chicago, November 1991.
- The Whitham Equations, NEEDS 1992, Dubna, Russia, July 1992.
- The Macroscopic Structure of Nonlinear Dispersive Oscillations, Colloquium, Michigan State University, February 1993.
- Hele-Shaw Flows, PDE Seminar, UC Berkeley, November 1993.
- A Cauchy Integral Approach to Hele-Shaw Problem, MSRI Seminar, March 1994.
- Hele-Shaw Flows, Colloquium, IUPUI, March 1994.
- A Cauchy Integral Approach to Hele-Shaw Problem, Colloquium, SUNY at Buffalo, October 1994.
- A Cauchy Integral Approach to Hele-Shaw Problem, Colloquium, Brown University, February 1995.
- A Cauchy Integral Approach to Hele-Shaw Problem, Colloquium, Ohio State University, February 1995.
- New Results on the Whitham Equations, Applied Math Seminar, Ohio State University, February 1995.
- Hele-Shaw Flows, Colloquium, UC Santa Cruz, March 1995.
- Lagrange Multipliers, Colloquium, UC Santa Cruz, March 1995.
- New Results on Hele-Shaw Flows, Colloquium, UC Davis, March 1995.
- Development of Singularities of Solutions of the Whitham Equations, the First Tianyan Conference on Mathematical Sciences, Berkeley, June 1997.
- The Semi-classical Limit of the Focusing NLS Equation, Applied Math Seminar, Duke University, March 1998.
- 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.
- New Results on the Focusing NLS, Applied Math Seminar, The Hong Kong University of Science and Technology, July 1999.
- Hele-Shaw Flows, Workshop on "Modeling of Pattern Formation and Material Interfaces", Beijing International Center for Computational Physics, Beijing, China, July 1999.
- The Whitham Equations, Applied Math Seminar, Qinghua University, Beijing, China, July 1999.
- Singularities in Hele-Shaw Flows, Applied Math Seminar, Chinese University of Hong Kong, August 1999.
- Hodograph Solutions of Whitham Type Equations, IMA workshop on "Dispersive Corrections to Transport Equations", May 2000.
- 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.
- 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.
- 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.
- 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.
- Phase Transition in KdV Oscillations, Dynamical Systems/Nonlinear Science Seminar, Princeton University, September 2001.
- Lax-Levermore-Venakides Minimization Problem, Colloquium, Rensselaer Polytechnic Institute, September 2001.
- Lax-Levermore-Venakides Minimization Problem, Analysis Seminar, Courant Institute, September 2001.
- Phase Transition in KdV Oscillations, Applied Math Seminar, UC Irvine, October 2001.
- Phase Transition in Dispersive Oscillations, Colloquium, Oklahoma State University, January 2002.
- Phase Transition in Dispersive Oscillations, Colloquium, Southern Methodist University, February 2002.
- Phase Transition in Dispersive Oscillations, Applied Math/PDE Seminar, University of Wisconsin at Madison, February 2002.
- Phase Transition in Dispersive Oscillations, Colloquium, University of Texas at Arlington, February 2002.
- Phase Transition in KdV Modulations, Special Session on "Partial Differential Equations" in 2002 AMS Central Section Meeting, Ann Arbor, Michigan, March 2002.
- Phase Transition in Dispersive Oscillations, PDE and Applied Math Seminar, University of Maryland, March 2002.
- 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.
- Phase Transition in KdV Oscillations, Colloquium, Wright State University, January 2003.
- Phase Transition in Dispersive Oscillations, Integrable Systems and Analysis Seminar, Duke University, February 2003.
- Dispersive Oscillations: An Overview, IMS Lecture, Chinese University of Hong Kong, February 2004.
- Phase Transition in Dispersive Oscillations, Applied Mathematics Seminar, Hong Kong University of Science and Technology, February 2004.
- Dispersive Oscillations: A Minimization Problem, IMS Lecture, Chinese University of Hong Kong, February 2004.
- New Results on Equilibrium Measure, Special Session on "Integrable Systems in Mathematics and Physics" in the 995th AMS meeting, Athens, Ohio, March 2004.
- Phase Transition in Dispersive Oscillations, PDEs and Numerical Methods Seminar, Penn State University, April 2004.
- Large Parameter Behavior of Equilibrium Measure, Geometry & Mathematical Physics Seminar, SISSA, Italy, June 2004.
- 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.
- Zero Dispersion Limits, PDE Seminar, OSU, March 2005.
- Zero Dispersion Limits, Colloquium, Zhongshan University, China, August 2005.
- 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.
- 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.
- Large Time Behavior of the Zero Dispersion Limit of the higher order KdV equation, PDE Seminar, OSU, May 2006.
- Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations, PDE Seminar, OSU, April 2007.
- Non-Strictly Hyperbolic Whitham Equations, PDE Seminar, IMS, Chinese University of Hong Kong, June 2007.
- Integrable Systems, Colloquium, Huang-Gang Normal University, June 2007.
- 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.
- Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation, Differential Equation Seminar, University of Michigan, March 2008.
- Initial Value Problem of the Whitham Equations for the Canassa-Holm Equation, Colloquium, Georgetown University, March 2009.
- 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.
- Initial Value Problem of the Modulation Equations
for the Camassa-Holm equation Colloquium, Shanghai Jiaotong University, June 2011.
- Weak Limits of Dispersive Oscillations and Their Dynamics, Colloquium, CMS, Zhejiang University, June 2011.
- 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.