Stephen Schecter

Works (30)

Updated: March 10th, 2025 12:14

2021 journal article

Geometric singular perturbation theory analysis of an epidemic model with spontaneous human behavioral change

JOURNAL OF MATHEMATICAL BIOLOGY, 82(6).

By: S. Schecter n

author keywords: Epidemiological modeling; Entry-exit function; Geometric singular perturbation theory; Imitation dynamics; Evolutionary game theory
MeSH headings : Behavior; Biological Evolution; Epidemics; Game Theory; Humans; Models, Biological
topics (OpenAlex): Mathematical and Theoretical Epidemiology and Ecology Models; COVID-19 epidemiological studies; Evolution and Genetic Dynamics
TL;DR: It is shown that the entry–exit function of geometric singular perturbation theory can be used to analyze the Poletti model in the limit in which behavior changes on a much faster time scale than that of the epidemic. (via Semantic Scholar)
Source: Web Of Science
Added: May 24, 2021

2021 article

MORE TRAVELING WAVES IN THE HOLLING-TANNER MODEL WITH WEAK DIFFUSION

Manukian, V., & Schecter, S. (2021, October). DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B.

By: V. Manukian* & S. Schecter n

author keywords: Geometric singular perturbation theory; traveling wave; compactifica-tion; prey-predator model; diffusive Holling-Tanner model; blow-up
topics (OpenAlex): Mathematical and Theoretical Epidemiology and Ecology Models; Differential Equations and Numerical Methods; Nonlinear Dynamics and Pattern Formation
Source: Web Of Science
Added: November 23, 2021

2018 journal article

Stability of combustion waves in a simplified gas-solid combustion model in porous media

By: F. Ozbag* & S. Schecter n

author keywords: travelling wave; stability; combustion waves; porous media
topics (OpenAlex): Advanced Mathematical Physics Problems; Stability and Controllability of Differential Equations; Nonlinear Dynamics and Pattern Formation
TL;DR: The essential spectrum of the linearized system at a travelling wave is determined and an extension of a recent result about partly parabolic systems that are stabilized by such weight functions is used to show nonlinear stability. (via Semantic Scholar)
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7. Affordable and Clean Energy (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2016 journal article

Stability of Concatenated Traveling Waves

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 28(3-4), 867–896.

By: X. Lin n & S. Schecter n

author keywords: Interaction of waves; Reaction-diffusion equation; Spatial dynamics; Laplace transform; Exponential dichotomy in trace space
topics (OpenAlex): Advanced Mathematical Modeling in Engineering; Stability and Controllability of Differential Equations; Mathematical and Theoretical Epidemiology and Ecology Models
Source: Web Of Science
Added: August 6, 2018

2016 journal article

The entry-exit function and geometric singular perturbation theory

JOURNAL OF DIFFERENTIAL EQUATIONS, 260(8), 6697–6715.

By: P. De Maesschalck* & S. Schecter n

author keywords: Entry-exit function; Geometric singular perturbation theory; Bifurcation delay; Blow-up; Turning point
topics (OpenAlex): Advanced Differential Equations and Dynamical Systems; Nonlinear Dynamics and Pattern Formation; stochastic dynamics and bifurcation
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Stability of concatenated traveling waves: Alternate approaches

JOURNAL OF DIFFERENTIAL EQUATIONS, 259(7), 3144–3177.

By: X. Lin n & S. Schecter n

author keywords: Traveling wave; Stability; Spatial dynamics; Laplace transform; Exponential dichotomy
topics (OpenAlex): Mathematical and Theoretical Epidemiology and Ecology Models; Nonlinear Differential Equations Analysis; Stability and Controllability of Differential Equations
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Travelling waves in the Holling-Tanner model with weak diffusion

By: A. Ghazaryan*, V. Manukian* & S. Schecter n

author keywords: geometric singular perturbation theory; travelling front; periodic wave train; predator-prey model; diffusive Holling-Tanner model; entry-exit function
topics (OpenAlex): Mathematical and Theoretical Epidemiology and Ecology Models; Evolution and Genetic Dynamics; Nonlinear Dynamics and Pattern Formation
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Combustion waves and Riemann solutions in light porous foam

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 11(2), 295–328.

By: G. Chapiro*, D. Marchesin* & S. Schecter n

author keywords: Traveling wave; Riemann problem; filtration combustion; combustion in porous media; ignition; extinction
topics (OpenAlex): Navier-Stokes equation solutions; Nonlinear Partial Differential Equations; Stability and Controllability of Differential Equations
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Morse theory for Lagrange multipliers and adiabatic limits

JOURNAL OF DIFFERENTIAL EQUATIONS, 257(12), 4277–4318.

By: S. Schecter n & G. Xu*

author keywords: Morse homology; Geometric singular perturbation theory; Exchange lemma; Adiabatic limit
topics (OpenAlex): Homotopy and Cohomology in Algebraic Topology; Geometric and Algebraic Topology; Geometry and complex manifolds
Source: Web Of Science
Added: August 6, 2018

2013 journal article

GASLESS COMBUSTION FRONTS WITH HEAT LOSS

SIAM JOURNAL ON APPLIED MATHEMATICS, 73(3), 1303–1326.

By: A. Ghazaryan*, S. Schecter n & P. Simon*

author keywords: geometric singular perturbation theory; traveling wave; Evans function; stability
topics (OpenAlex): Differential Equations and Numerical Methods; Combustion and flame dynamics; stochastic dynamics and bifurcation
TL;DR: For a model of gasless combustion with heat loss, geometric singular perturbation theory is used to show existence of traveling combustion fronts and it is shown that the fronts are nonlinearly stable in an appropriate sense if an Evans function criterion is satisfied. (via Semantic Scholar)
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7. Affordable and Clean Energy (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Stability of Traveling Waves in Partly Parabolic Systems

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 8(5), 31–47.

By: A. Ghazaryan*, Y. Latushkin* & S. Schecter n

author keywords: traveling wave; spectral stability; linear stability; nonlinear stability; exponential weights
topics (OpenAlex): Stability and Controllability of Differential Equations; Nonlinear Dynamics and Pattern Formation; Advanced Mathematical Modeling in Engineering
Source: Web Of Science
Added: August 6, 2018

2012 journal article

DAFERMOS REGULARIZATION OF A DIFFUSIVE-DISPERSIVE EQUATION WITH CUBIC FLUX

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 32(12), 4069–4110.

By: S. Schecter* & M. Taylor

author keywords: Riemann solution; undercompressive shock wave; geometric singular perturbation theory; exponential dichotomy
topics (OpenAlex): Advanced Mathematical Physics Problems; Computational Fluid Dynamics and Aerodynamics; Navier-Stokes equation solutions
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Heteroclinic Orbits in Slow-Fast Hamiltonian Systems with Slow Manifold Bifurcations

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 22(4), 629–655.

By: S. Schecter n & C. Sourdis*

author keywords: Geometric singular perturbation theory; Blow-up; Pitchfork bifurcation; Transcritical bifurcation
topics (OpenAlex): Quantum chaos and dynamical systems; Theoretical and Computational Physics; Spectroscopy and Quantum Chemical Studies
Source: Web Of Science
Added: August 6, 2018

2010 journal article

STABILITY OF TRAVELING WAVES FOR A CLASS OF REACTION-DIFFUSION SYSTEMS THAT ARISE IN CHEMICAL REACTION MODELS

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 42(6), 2434–2472.

By: A. Ghazaryan, Y. Latushkin & S. Schecter*

author keywords: traveling wave; nonlinear stability; reaction-diffusion system; degenerate diffusion matrix; weighted norm; combustion
topics (OpenAlex): Stability and Controllability of Differential Equations; Advanced Mathematical Modeling in Engineering; Quantum chaos and dynamical systems
TL;DR: Perturbations of the wave in $H^1$ or $BUC$ that are small in both the weighted norm and the un Weighted norm are shown to stay small in the unweighted norm and to decay exponentially to a shift of the traveling wave in the weightednorm. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Stability of Gasless Combustion Fronts in One-Dimensional Solids

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 198(3), 981–1030.

By: A. Ghazaryan*, Y. Latushkin*, S. Schecter n & A. Souza*

topics (OpenAlex): Stability and Controllability of Differential Equations; Numerical methods in inverse problems; Advanced Mathematical Modeling in Engineering
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Persistence of Rarefactions under Dafermos Regularization: Blow-Up and an Exchange Lemma for Gain-of-Stability Turning Points

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 8(3), 822–853.

By: S. Schecter* & P. Szmolyan*

author keywords: conservation laws; Riemann problem; geometric singular perturbation theory; loss of normal hyperbolicity; blow-up
topics (OpenAlex): Navier-Stokes equation solutions; Cosmology and Gravitation Theories; Stability and Controllability of Differential Equations
TL;DR: Self-similar solutions of the Dafermos regularization of a system of conservation laws near structurally stable Riemann solutions composed of Lax shocks and rarefactions are constructed, with all waves possibly large. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Travelling waves for a thin liquid film with surfactant on an inclined plane

NONLINEARITY, 22(1), 85–122.

By: V. Manukian n & S. Schecter n

topics (OpenAlex): Fluid Dynamics and Thin Films; Nonlinear Dynamics and Pattern Formation; Surfactants and Colloidal Systems
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UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2008 journal article

Exchange lemmas 1: Deng's lemma

JOURNAL OF DIFFERENTIAL EQUATIONS, 245(2), 392–410.

By: S. Schecter n

author keywords: geometric singular perturbation theory; normally hyperbolic invariant manifold
topics (OpenAlex): Stability and Controllability of Differential Equations; Nonlinear Differential Equations Analysis; Mathematical and Theoretical Epidemiology and Ecology Models
Source: Web Of Science
Added: August 6, 2018

2008 journal article

Exchange lemmas 2: General Exchange Lemma

JOURNAL OF DIFFERENTIAL EQUATIONS, 245(2), 411–441.

By: S. Schecter n

author keywords: geometric singular perturbation theory; normally hyperbolic invariant manifold
topics (OpenAlex): Quantum chaos and dynamical systems; Advanced Differential Equations and Dynamical Systems; Stability and Controllability of Differential Equations
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Combustion fronts in a porous medium with two layers

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 18(3), 615–665.

By: J. Da Mota* & S. Schecter n

author keywords: reaction-diffusion-convection system; traveling wave; nonhyperbolic equilibrium; geometric singular perturbation theory; Melnikov integral
topics (OpenAlex): Combustion and flame dynamics; Differential Equations and Numerical Methods; Nonlinear Dynamics and Pattern Formation
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Eigenvalues of self-similar solutions of the dafermos regularization of a system of conservation laws via geometric singular perturbation theory

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 18(1), 53–101.

By: S. Schecter n

author keywords: conservation law; Dafermos regularization; eigenfunction; eigenvalue; geometric singular perturbation theory; Riemann problem; stability
topics (OpenAlex): Navier-Stokes equation solutions; Differential Equations and Numerical Methods; Numerical methods in inverse problems
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UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2004 journal article

Computation of Riemann solutions using the Dafermos regularization and continuation

Discrete and Continuous Dynamical Systems, 10(4), 965–986.

By: S. Schecter*, B. Plohr & D. Marchesin

topics (OpenAlex): Navier-Stokes equation solutions; Computational Fluid Dynamics and Aerodynamics; Gas Dynamics and Kinetic Theory
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UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: NC State University Libraries
Added: August 6, 2018

2004 journal article

Existence of Dafermos profiles for singular shocks

Journal of Differential Equations, 205(1), 185–210.

By: S. Schecter

topics (OpenAlex):
Source: NC State University Libraries
Added: August 6, 2018

2003 journal article

Oxidation heat pulses in two-phase expansive flow in porous media

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 54(1), 48–83.

By: D. Marchesin & S. Schecter n

author keywords: combustion; porous media; multiphase flow; conservation laws
topics (OpenAlex): Hydrocarbon exploration and reservoir analysis; Petroleum Processing and Analysis; Enhanced Oil Recovery Techniques
Source: Web Of Science
Added: August 6, 2018

2003 journal article

Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 35(4), 884–921.

By: X. Lin* & S. Schecter*

author keywords: conservation law; Riemann problem; Dafermos regularization; stability; spectrum; singular perturbation
topics (OpenAlex): Navier-Stokes equation solutions; Cosmology and Gravitation Theories; Advanced Mathematical Physics Problems
TL;DR: It is shown, by studying the essential spectrum of the linearized system in a weighted function space, that stability is determ ined by eigenvalues only. (via Semantic Scholar)
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UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Traveling-wave solutions of convection-diffusion systems by center manifold reduction

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 49(1), 35–59.

By: S. Schecter n

author keywords: convection-diffusion systems; nonconservation form; traveling waves; shock waves; center manifold reduction
topics (OpenAlex): Differential Equations and Numerical Methods; Fractional Differential Equations Solutions; Mathematical and Theoretical Epidemiology and Ecology Models
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2002 journal article

Undercompressive shock waves and the Dafermos regularization

NONLINEARITY, 15(4), 1361–1377.

By: S. Schecter n

topics (OpenAlex): Navier-Stokes equation solutions; Advanced Mathematical Physics Problems; Cosmology and Gravitation Theories
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2001 journal article

Geometric singular perturbation analysis of oxidation heat pulses for two-phase flow in porous media

BOLETIM DA SOCIEDADE BRASILEIRA DE MATEMATICA, 32(3), 237–270.

By: S. Schecter n & D. Marchesin

author keywords: combustion; porous medium; multiphase flow; conservation laws
topics (OpenAlex): Differential Equations and Numerical Methods; Advanced Mathematical Modeling in Engineering; Radiative Heat Transfer Studies
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
13. Climate Action (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

1999 journal article

Codimension-one Riemann solutions: Classical missing rarefaction cases

JOURNAL OF DIFFERENTIAL EQUATIONS, 157(2), 247–318.

By: S. Schecter n

author keywords: conservation law; Riemann problem; viscous profile
topics (OpenAlex): Navier-Stokes equation solutions; Geometric Analysis and Curvature Flows; Nonlinear Partial Differential Equations
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

1997 journal article

An organizing center for wave bifurcation in multiphase flow models

SIAM Journal on Applied Mathematics, 57(5), 1189–1215.

By: D. Marchesin, B. Plohr & S. Schecter*

topics (OpenAlex): Navier-Stokes equation solutions; Fluid Dynamics and Turbulent Flows; Computational Fluid Dynamics and Aerodynamics
TL;DR: This paper uses singularity theory and bifurcation theory of dynamical systems, including Melnikov's method, to find all nearby shock waves that are admissible according to the viscous profile criterion and constructs a unique solution of the Riemann problem for each left and right state and parameter value in a neighborhood of the unperturbed shock wave solution. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: NC State University Libraries
Added: August 6, 2018

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