Stephen Schecter

Professor Emeritus

Department of Mathematics
North Carolina State University
Raleigh, NC 27695-8205

e-mail: schecter@ncsu.edu

Curriculum Vita (July 2022)

Published July 2021! Free e-book from IMPA!

Published April 2016! Check out the book's web page.

Teaching

MA 440-001 (Game Theory) Fall 2016
MA 303-001 Spring 2016
MA 440-001 (Game Theory) Fall 2015
MA 341-004 Spring 2015
MA 440-001 (Game Theory) Fall 2014: syllabus, schedule, text
MA 793 (Stability of Traveling Waves) Spring 2014
MA 114-003 Fall 2013
MA 440-001 (Game Theory) Fall 2013
MA 732-001 Spring 2013
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, epidemiology

Some other topics I've worked on

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

Some 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)
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)
Concatenated Traveling Waves (Equadiff 2015, Lyon, France, July 6-10, 2015)
How the Talmud Divides an Estate Among Creditors (expository talk at Miami University, Sept. 23, 2016)
The Entry-Exit Function and Geometric Singular Perturbation Theory (Miami University, Sept. 24, 2016)
A Game Theory Course for Mathematics Students (SIAM Conference on Applied Mathematics Education, Philadelphia, Oct. 1, 2016)

Papers since 1996

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) doi: 10.1023/A:1015126703505 (pdf file)
Classification of Codimension-One Riemann Solutions (with B. Plohr and D. Marchesin, J. Dynam. Differential Equations 13 (2001), 523-588) doi: 10.1023/A:1016634307145 (pdf file)
Traveling-Wave Solutions of Convection-Diffusion Equations by Center Manifold Reduction (Nonlinear Analysis: Theory, Methods & Applications 49 (2002), 35-59) doi: 10.1016/S0362-546X(01)00097-9 (pdf file)
Codimension-One Riemann Solutions: Missing Rarefactions Adjacent to Doubly Sonic Transitional Waves (J. Dynam. Differential Equations 14 (2002), 295 - 348) doi: 10.1023/A:1015126703505 (pdf file)
Undercompressive Shock Waves and the Dafermos Regularization (Nonlinearity 15 (2002), 1361 - 1377) doi: 10.1088/0951-7715/15/4/318 (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) doi: 10.1007/BF01233667 (ps file)
Oxidation Heat Pulses in Two-Phase Expansive Flow in Porous Media (with D. Marchesin, ZAMP 54 (2003), 48 - 83) doi: 10.1007/PL00012634 (pdf file)
Steam Condensation Waves in Water-Saturated Porous Rock (with J. Bruining and D. Marchesin, Qual. Theory Dyn. Syst. 4 (2003), 205 - 231) doi: 10.1007/BF02970859 (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) doi: 10.1137/S0036141002405029 (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) doi: 10.3934/dcds.2004.10.965 (pdf file)
Existence of Dafermos Profiles for Singular Shocks (J. Differential Eqs. 205 (2004), 185 - 210) doi: 10.1016/j.jde.2004.06.013 (pdf file)
Composite Waves in the Dafermos Regularization (with P. Szmolyan, J. Dynam. Differential Equations 16 (2004), 847 - 867) doi: 10.1007/s10884-004-6698-2 (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) doi: 10.1007/s10884-005-9000-3 (pdf file)
Combustion Fronts in a Porous Medium with Two Layers (with J. C. da Mota, J. Dynam. Differential Equations 18 (2006), 615 - 665) doi: 10.1007/s10884-006-9019-0 (pdf file)
Exchange Lemmas 1: Deng's Lemma (J. Differential Eqs. 245 (2008), 392 - 410) doi: 10.1016/j.jde.2007.08.011 (pdf file)
Exchange Lemmas 2: General Exchange Lemma (J. Differential Eqs. 245 (2008), 411 - 441) doi: 10.1016/j.jde.2007.10.021 (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) doi: 10.1137/080715305 (pdf file)
Traveling Waves for a Thin Liquid Film with Surfactant on an Inclined Plane (with Vahagn Manukian, Nonlinearity 22 (2009), 85-122) doi: 10.1088/0951-7715/22/1/006 (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) doi: 10.1007/s00205-010-0358-y (pdf file)
Heteroclinic Orbits in Slow-Fast Hamiltonian Systems with Slow Manifold Bifurcations (with Christos Sourdis, J. Dynam. Differential Equations 22 (2010), 629 - 655) doi: 10.1007/s10884-010-9171-4 (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) doi: 10.1512/iumj.2011.60.4069 (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) doi: 10.1137/100786204 (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) doi: 10.3934/dcds.2012.32.4069 (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 doi: 10.1007/978-1-4614-4559-3 (pdf file)
Gasless Combustion Fronts with Heat Loss (with Anna Ghazaryan and Peter L. Simon, SIAM J. Appl. Math. 73 (2013), 1303 - 1326) doi: 10.1137/110854540 (pdf file)
Stability of Traveling Waves in Partly Parabolic Systems (review article with Anna Ghazaryan and Yuri Latushkin, Math. Model. Nat. Phenom. 8 (2013), 31 - 47) doi: 10.1051/mmnp/20138503 (pdf file)
Combustion Waves and Riemann Solutions in Light Porous Foam (with Grigori Chapiro and Dan Marchesin, J. Hyperbolic Differ. Equ. 11 (2014), 295 - 328) doi: 10.1142/S021989161450009X (pdf file)
Morse Theory for Lagrange Multipliers and Adiabatic Limits (with Guangbo Xu, J. Differential Eqs. 257 (2014), 4277 - 4318) doi: 10.1016/j.jde.2014.08.018 (pdf file)
Stability of Concatenated Traveling Waves: Alternate Approaches (with Xiao-Biao Lin, J. Differential Equations 259 (2015), 3144 - 3177) doi: 10.1016/j.jde.2015.04.015 (pdf file)
Traveling Waves in the Holling-Tanner Model with Weak Diffusion (with Anna Ghazaryan and Vahagn Manukian, Proc. Roy. Soc. London Ser. A 471 (2015): 20150045) doi: 10.1098/rspa.2015.0045 (pdf file)
The Entry-Exit Function and Geometric Singular Perturbation Theory (with Peter De Maesschalck, J. Differential Eqs. 260 (2016), 6697 - 6715) doi: 10.1016/j.jde.2016.01.008 (pdf file)
Traveling Waves in a Simplified Gas-Solid Combustion Model in Porous Media (with F. Ozbag and G. Chapiro, Adv. Differential Equations 23 (2018), 409 - 454) (pdf file)
Stability of Combustion Waves in a Simplified Gas-Solid Combustion Model in Porous Media (with F. Ozbag, Philos. Trans. Roy. Soc. A 376 (2018), no. 2117, 20170185, 19 pp.) doi: 10.1098/rsta.2017.0185 (pdf file)
More Traveling Waves in the Holling-Tanner Model with Weak Diffusion (with Vahagn Manukian, Discrete Contin. Dyn. Syst. B 27 (2021), 4875 - 4890) doi: 10.3934/dcdsb.2021256 (pdf file)
Geometric Singular Perturbation Theory Analysis of an Epidemic Model with Spontaneous Human Behavioral Change (J. Math. Biol. 82 (2021)) doi: 10.1007/s00285-021-01605-2 (pdf file)

Revised: Aug 2, 2022