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Works (30)
Updated: August 16th, 2024 13:37
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)
open access via link.springer.com (publisher PDF)
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.
author keywords: Geometric singular perturbation theory; traveling wave; compactifica-tion; prey-predator model; diffusive Holling-Tanner model; blow-up
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
The entry-exit function and geometric singular perturbation theory
JOURNAL OF DIFFERENTIAL EQUATIONS, 260(8), 6697–6715.
author keywords: Entry-exit function; Geometric singular perturbation theory; Bifurcation delay; Blow-up; Turning point
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
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 28(3-4), 867–896.
author keywords: Interaction of waves; Reaction-diffusion equation; Spatial dynamics; Laplace transform; Exponential dichotomy in trace space
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.
author keywords: Traveling wave; Stability; Spatial dynamics; Laplace transform; Exponential dichotomy
Source: Web Of Science
Added: August 6, 2018
2015 journal article
Travelling waves in the Holling-Tanner model with weak diffusion
author keywords: geometric singular perturbation theory; travelling front; periodic wave train; predator-prey model; diffusive Holling-Tanner model; entry-exit function
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.
author keywords: Traveling wave; Riemann problem; filtration combustion; combustion in porous media; ignition; extinction
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.
author keywords: Morse homology; Geometric singular perturbation theory; Exchange lemma; Adiabatic limit
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.
author keywords: traveling wave; spectral stability; linear stability; nonlinear stability; exponential weights
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.
author keywords: Riemann solution; undercompressive shock wave; geometric singular perturbation theory; exponential dichotomy
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.
author keywords: Geometric singular perturbation theory; Blow-up; Pitchfork bifurcation; Transcritical bifurcation
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
2008 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
2007 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
2007 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.
author keywords: reaction-diffusion-convection system; traveling wave; nonhyperbolic equilibrium; geometric singular perturbation theory; Melnikov integral
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.
author keywords: conservation law; Dafermos regularization; eigenfunction; eigenvalue; geometric singular perturbation theory; Riemann problem; stability
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.
author keywords: convection-diffusion systems; nonconservation form; traveling waves; shock waves; center manifold reduction
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.
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 Goal Categories
15. Life on Land
(OpenAlex)
Source: NC State University Libraries
Added: August 6, 2018
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