Stephen Schecter Professor Department of Mathematics North Carolina State University Raleigh, NC 27695-8205 e-mail: schecter@math.ncsu.edu Office: SAS 3226 Office hours (Spring 2013): MTWHF 10:15 a.m. - 11:05 a.m. Telephone: 919 515 6533 Fax: 919 513 7336 Curriculum Vita (January 2013)

Teaching

• Spring 2013
  
  
  • MA 732-001 Ordinary Differential Equations II
  
  
• Earlier Semesters
  
  
  • MA 440-001 (Game Theory) Fall 2012
  • MA 532-001 Fall 2012
  • MA 341-007 Spring 2012
  • MA 225-002 Fall 2011
  • MA 440-001 (Game Theory) Fall 2011
  • MA 341-007 Spring 2011
  • MA 114-001 Fall 2009
  • MA 732-001 Spring 2009
  • MA 532-001 Fall 2008
  • MA 341H-001 Fall 2007
  • MA 425-002 Spring 2006
  • MA 103Q-002 (Topics in Contemporary Mathematics: Mathematics and Politics) Spring 2004
  • MA 242-005 Fall 2003
  • MA 426-001/MA 591M-001 Spring 2003
  • MA 103-005 Fall 2002

Current research interests

• Traveling waves and their stability, geometric singular perturbation theory

Some other topics I've worked on

• Shock waves and Riemann solutions
• Homoclinic and heteroclinic bifurcation
• Averaging
• Polynomial vector fields
• Mathematical economics

Some recent talks

• Combustion Fronts in Porous Media with Two Layers (SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, May 22 - 26, 2005)
• Traveling Waves in a Thin Film with Surfactant (International Conference on Dynamics in Perturbations on the Occasion of Freddy Dumortier's 60th Birthday, University of Hasselt, Belgium, April 23 - 27, 2007)
• Stability of Patterns (10th Workshop on Partial Differential Equations, IMPA, Rio de Janeiro, August 7, 2007)
• Stability of Fronts in Gasless Combustion (International Conference on Infinite Dimensional Dynamical Systems, Toronto, Sept. 24 - 28, 2008)
• Game Theory and Global Warming (short course at SACNAS National Conference, Oct. 9 -- 12, 2008)
• How the Talmud Divides an Estate Among Creditors (expository talk at Brigham Young University, Mar. 16, 2009)
• Exchange Lemmas (SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, May 17 - 21, 2009)
• Heteroclinic Solutions of a Singularly Perturbed Hamiltonian System (AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden, May 25, 2010)
• Stability of Traveling Waves for a Class of Reaction-Diffusion Systems that Arise in Chemical Reaction Models (Joint SIAM/RSME-SCM-SEMA Meeting on Emerging Topics in Dynamical Systems and Partial Differential Equations, Barcelona, June 3, 2010)
• Exchange Lemmas (IMA New Directions Short Course: Invariant Objects in Dynamical Systems and their Applications, Minneapolis, June 20 - July 1, 2011)
• Loss of Normal Hyperbolicity (IMA New Directions Short Course: Invariant Objects in Dynamical Systems and their Applications, Minneapolis, June 20 - July 1, 2011)
• Morse Theory, Lagrange Multipliers, and Geometric Singular Perturbation Theory (Dynamics of Differential Equations, Atlanta, March 16 - 20, 2013)

Recent papers

• Structurally Stable Riemann Solutions (with B. Plohr and D. Marchesin, J. Differential Eqs. 126 (1996), 303-354) (pdf file)
• An Organizing Center for Wave Bifurcation in Multiphase Flow Models (with B. Plohr and D. Marchesin, SIAM J. Appl. Math. 57 (1997), 1189-1215) (pdf file)
• Codimension-One Riemann Solutions: Classical Missing Rarefaction Cases (J. Differential Eqs. 157 (1999), 257-318) (pdf file)
• Codimension-One Riemann Solutions: Missing Rarefactions in Transitional Wave Groups (Advances in Differential Equations 5 (2000), 929-975) (pdf file)
• Classification of Codimension-One Riemann Solutions (with B. Plohr and D. Marchesin, J. Dynam. Differential Equations 13 (2001), 523-588) (pdf file)
• Traveling-Wave Solutions of Convection-Diffusion Equations by Center Manifold Reduction (Nonlinear Analysis: Theory, Methods & Applications 49 (2002), 35-59) (pdf file)
• Codimension-One Riemann Solutions: Missing Rarefactions Adjacent to Doubly Sonic Transitional Waves (J. Dynam. Differential Equations 14 (2002), 295 - 348) (pdf file)
• Undercompressive Shock Waves and the Dafermos Regularization (Nonlinearity 15 (2002), 1361 - 1377) (pdf file)
• Geometric Singular Perturbation Analysis of Oxidation Heat Pulses for Two-Phase Flow in Porous Media (with D. Marchesin, Bulletin of the Brazilian Mathematical Society 32 (2002), 237-270) (ps file)
• Oxidation Heat Pulses in Two-Phase Expansive Flow in Porous Media (with D. Marchesin, ZAMP 54 (2003), 48 - 83) (pdf file)
• Steam Condensation Waves in Water-Saturated Porous Rock (with J. Bruining and D. Marchesin, Qual. Theory Dyn. Syst. 4 (2003), 205 - 231) (pdf file)
• Stability of Self-Similar Solutions of the Dafermos Regularization of a System of Conservation Laws (with X.-B. Lin, SIAM J. Math. Anal. 35 (2003), 884-921) (pdf file)
• Computation of Riemann Solutions Using the Dafermos Regularization and Continuation (with B. Plohr and D. Marchesin, Discrete Contin. Dyn. Syst. 10 (2004), 965-986) (pdf file)
• Existence of Dafermos Profiles for Singular Shocks (J. Differential Eqs. 205 (2004), 185 - 210) (pdf file)
• Composite Waves in the Dafermos Regularization (with P. Szmolyan, J. Dynam. Differential Equations 16 (2004), 847 - 867) (pdf file)
• Eigenvalues of Self-Similar Solutions of the Dafermos Regularization of a System of Conservation Laws via Geometric Singular Perturbation Theory (J. Dynam. Differential Equations 18 (2006), 53 - 101) (pdf file)
• Combustion Fronts in a Porous Medium with Two Layers (with J. C. da Mota, J. Dynam. Differential Equations 18 (2006), 615 - 665) (pdf file)
• Exchange Lemmas 1: Deng's Lemma (J. Differential Eqs. 245 (2008), 392 - 410) (pdf file)
• Exchange Lemmas 2: General Exchange Lemma (J. Differential Eqs. 245 (2008), 411 - 441) (pdf file)
• Persistence of Rarefactions under Dafermos Regularization: Blow-up and an Exchange Lemma for Gain-of-Stability Turning Points (with Peter Szmolyan, SIAM J. Appl. Dyn. Syst. 8 (2009), 822 -853) (pdf file)
• Traveling Waves for a Thin Liquid Film with Surfactant on an Inclined Plane (with Vahagn Manukian, Nonlinearity 22 (2009), 85-122) (pdf file)
• Stability of Gasless Combustion Fronts in One-dimensional Solids (with Anna Ghazaryan, Yuri Latushkin, and Aparecido J. de Souza, Arch. Ration. Mech. Anal. 198 (2010), 981 - 1030) (pdf file)
• Heteroclinic Orbits in Slow-Fast Hamiltonian Systems with Slow Manifold Bifurcations (with Christos Sourdis, J. Dynam. Differential Equations 22 (2010), 629 - 655) (pdf file)
• Stability of Traveling Waves for Degenerate Systems of Reaction-Diffusion Equations (with Anna Ghazaryan and Yuri Latushkin, Indiana Univ. Math. J. 60 (2011), 443 - 472)(pdf file)
• Stability of Traveling Waves for a Class of Reaction-Diffusion Systems that Arise in Chemical Reaction Models (with Anna Ghazaryan and Yuri Latushkin, SIAM J. Math. Anal. 42 (2010), 2434 - 2472) (pdf file)
• Dafermos Regularization of a Diffusive-Dispersive Equation with Cubic Flux (with Monique Richardson Taylor, Discrete Contin. Dyn. Syst. A 32 (2012), 4069 - 4110) (pdf file)
• How the Talmud Divides an Estate Among Creditors, expository article in Bridging Mathematics, Statistics, Engineering and Technology: Contributions from the Seminar on Mathematical Sciences and Applications, Springer, 2012 (pdf file)
• Gasless Combustion Fronts with Heat Loss (with Anna Ghazaryan and Peter L. Simon), revised January 2013, to appear in SIAM J. App. Math. (pdf file)
• Morse Theory for Lagrange Multipliers and Adiabatic Limits (with Guangbo Xu), preprint, January 2013 (pdf file)
• Stability of Traveling Waves in Partly Parabolic Systems (review article with Anna Ghazaryan and Yuri Latushkin), to appear in Math. Model. Nat. Phenom. (pdf file)