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Updated: April 4th, 2024 21:51

2021 journal article

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

*JOURNAL OF MATHEMATICAL BIOLOGY*, *82*(6).

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

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)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science; OpenAlex)

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*.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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

author keywords: travelling wave; stability; combustion waves; porous media

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)

UN Sustainable Development Goal Categories

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.

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.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Travelling waves in the Holling-Tanner model with weak diffusion

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

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.

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.

author keywords: geometric singular perturbation theory; traveling wave; Evans function; stability

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)

UN Sustainable Development Goal Categories

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.

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.

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.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

author keywords: traveling wave; nonlinear stability; reaction-diffusion system; degenerate diffusion matrix; weighted norm; combustion

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.

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.

author keywords: conservation laws; Riemann problem; geometric singular perturbation theory; loss of normal hyperbolicity; blow-up

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)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

author keywords: geometric singular perturbation theory; normally hyperbolic invariant manifold

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

author keywords: geometric singular perturbation theory; normally hyperbolic invariant manifold

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

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.

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.

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.

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.

author keywords: combustion; porous media; multiphase flow; conservation laws

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.

author keywords: conservation law; Riemann problem; Dafermos regularization; stability; spectrum; singular perturbation

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)

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.

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.

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.

author keywords: combustion; porous medium; multiphase flow; conservation laws

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

author keywords: conservation law; Riemann problem; viscous profile

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.

UN Sustainable Development Goal Categories

15. Life on Land
(OpenAlex)

Source: NC State University Libraries

Added: August 6, 2018

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