Stephen Schecter Professor Department of Mathematics North Carolina State University Raleigh, NC 27695-8205 e-mail: schecter@math.ncsu.edu Office: 349 Harrelson Hall Office hours (Spring 2008): MWF 11:20 a.m. - 12:10 a.m., TH 9:10 a.m. - 10:00 a.m. Telephone: 919 515 6533 Fax: 919 513 7336 Curriculum Vita (February 2007)

Teaching

• Spring 2008
  
  
  • MA 341-001
  
  
• Earlier Semesters
  
  
  • MA 440-001 (Game Theory) Fall 2007
  • MA 341H-001 Fall 2007
  • MA 493B-001 (Game Theory) Fall 2006
  • MA 341-003 Fall 2006
  • MA 341-001 Spring 2006
  • MA 425-002 Spring 2006
  • MA 425-002 Fall 2005
  • MA 493B-003 (Game Theory) Fall 2005
  • MA 225-001 Spring 2005
  • MA 341-005 Spring 2005
  • MA 114-001 Fall 2004
  • MA 225-003 Fall 2004
  • MA 103Q-002 (Topics in Contemporary Mathematics: Mathematics and Politics) Spring 2004
  • MA 732-001 Spring 2004
  • MA 242-005 Fall 2003
  • MA 532-001 Fall 2003
  • MA 425-003 Spring 2003
  • MA 426-001/MA 591M-001 Spring 2003
  • MA 103-005 Fall 2002
  • MA 426-003/MA 591M-003 Fall 2002

Current research interests

• Shock waves, traveling waves, geometric singular perturbation theory

Some other topics I've worked on

• 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)
• Exchange Lemmas (Dynamical Systems Weekend on the Occasion of Carmen Chicone's 60th Birthday, Columbia, Missouri, May 19 - 21, 2006)
• 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 (Seminar, University of Missouri, May 8, 2008)

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 (2004), 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, to appear in J. Differential Eqs. (pdf file)
• Exchange Lemmas 2: General Exchange Lemma, to appear in J. Differential Eqs. (pdf file)
• Rarefactions in the Dafermos Regularization of a System of Conservation Laws (with Peter Szmolyan), preprint, March 2007 (pdf file)
• Traveling Waves for a Thin Liquid Film with Surfactant on an Inclined Plane (with Vahagn Manukian), preprint, April 2008 (pdf file)