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Tian, Fei-Ran

Office:MW 418 (Columbus)
Phone:614-292-0852 (Columbus)
Email:
Website:http://www.math.ohio-state.edu/~tian
OSU ID:tian.5
Research Areas:Partial Differential Equations
zero dispersion or semi-classical limits, Whitham equations, modulation of dispersive oscillations, hyperbolic consevation laws, free boundary problems.
Teaching:View Teaching Schedule

Office Hours
by appointment

Selected Publications

  1. (with V. Pierce) ``Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations for the KdV Hierarchy'', Dynamics of PDE, 4(2007), 263-282.
  2. (with V. Pierce) ``Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation'', Dynamics of PDE, 4(2007), 87-109.
  3. (with V. Pierce) ``Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations'', Comm. Math. Sci. 4(2006), 799-822.
  4. (with T. Grava) ``Large Parameter Behavior of Equilibrium Measure'', Comm. Math. Sci. 4(2006), 551-573.
  5. (with T. Grava) ``The Generation, Propagation and Extinction of Multiphases in the KdV Zero Dispersion Limit'', Comm. Pure Appl. Math. 55(2002), 1569-1639.
  6. (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.
  7. (with M. Shelley, K. Wlodarski) ``Hele-Shaw Flows and Pattern Formation in a Time-Dependent Gap'', Nonlinearity 10(1997), 1471-1495.
  8. ``Oscillations of the Zero Dispersion Limit of the Korteweg-de Vries Equation'', Comm. Pure Appl.Math. 46(1993), 1093-1129.