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Author ID: szmolyan.peter Recent zbMATH articles by "Szmolyan, Peter"
Published as: Szmolyan, Peter; Szmolyan, P.
External Links: MGP

Publications by Year

Citations contained in zbMATH Open

46 Publications have been cited 1,318 times in 672 Documents Cited by Year
Extending geometric singular perturbation theory to nonhyperbolic points – fold and canard points in two dimensions. Zbl 1002.34046
Krupa, M.; Szmolyan, P.
245
2001
Relaxation oscillation and canard explosion. Zbl 0994.34032
Krupa, M.; Szmolyan, P.
210
2001
Canards in \(\mathbb{R}^3\). Zbl 1007.34057
Szmolyan, Peter; Wechselberger, Martin
149
2001
Extending slow manifolds near transcritical and pitchfork singularities. Zbl 0998.34039
Krupa, M.; Szmolyan, P.
71
2001
Transversal heteroclinic and homoclinic orbits in singular perturbation problems. Zbl 0734.34038
Szmolyan, P.
66
1991
Relaxation oscillations in \({\mathbb R}^3\). Zbl 1058.34055
Szmolyan, P.; Wechselberger, M.
62
2004
Fast and slow waves in the FitzHugh-Nagumo equation. Zbl 0898.34050
Krupa, Martin; Sandstede, Björn; Szmolyan, Peter
62
1997
Existence and bifurcation of viscous profiles for all intermediate magnetohydrodynamic shock waves. Zbl 0817.34028
Freistühler, H.; Szmolyan, P.
36
1995
Geometry of mixed-mode oscillations in the 3-D autocatalator. Zbl 0933.92036
Milik, Alexandra; Szmolyan, Peter; Löffelmann, Helwig; Gröller, Eduard
34
1998
Geometric singular perturbation analysis of an autocatalator model. Zbl 1362.34076
Gucwa, Ilona; Szmolyan, Peter
33
2009
Scaling in singular perturbation problems: blowing up a relaxation oscillator. Zbl 1243.34066
Kosiuk, Ilona; Szmolyan, Peter
30
2011
Spectral stability of small shock waves. Zbl 1018.35010
Freistühler, H.; Szmolyan, P.
30
2002
A geometric singular perturbation analysis of detonation and deflagration waves. Zbl 0783.76099
Gasser, I.; Szmolyan, P.
24
1993
Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle. Zbl 1344.34068
Kosiuk, Ilona; Szmolyan, Peter
24
2016
Asymptotic expansions using blow-up. Zbl 1081.34052
van Gils, S.; Krupa, M.; Szmolyan, P.
21
2005
Multiscale geometry of the Olsen model and non-classical relaxation oscillations. Zbl 1321.34065
Kuehn, Christian; Szmolyan, Peter
21
2015
Geometric analysis of the singularly perturbed planar fold. Zbl 1013.34057
Krupa, M.; Szmolyan, P.
19
2001
A system of convection-diffusion equations with small diffusion coefficient arising in semiconductor physics. Zbl 0709.35058
Markowich, Peter A.; Szmolyan, Peter
17
1989
Multiple time scales and canards in a chemical oscillator. Zbl 1013.34044
Milik, Alexandra; Szmolyan, Peter
17
2001
Spectral stability of small-amplitude viscous shock waves in several space dimensions. Zbl 1188.35117
Freistühler, Heinrich; Szmolyan, Peter
14
2010
Composite waves in the Dafermos regularization. Zbl 1076.35074
Schecter, Stephen; Szmolyan, Peter
14
2004
Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations. Zbl 1380.37105
Hayes, Michael G.; Kaper, Tasso J.; Szmolyan, Peter; Wechselberger, Martin
13
2016
Bifurcation of traveling waves in extrinsic semiconductors. Zbl 0960.34031
Katzengruber, B.; Krupa, M.; Szmolyan, P.
11
2000
A geometric analysis of the Lagerstrom model problem. Zbl 1059.34033
Popović, Nikola; Szmolyan, Peter
10
2004
Geometric singular perturbation analysis of the Yamada model. Zbl 1106.34027
Huber, A.; Szmolyan, P.
9
2005
Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit. Zbl 1477.34074
Uldall Kristiansen, K.; Szmolyan, P.
9
2021
Rigorous asymptotic expansions for Lagerstrom’s model equation – a geometric approach. Zbl 1082.34045
Popović, Nikola; Szmolyan, Peter
8
2004
Singular perturbation analysis of a regularized MEMS model. Zbl 1458.34103
Iuorio, Annalisa; Popović, Nikola; Szmolyan, Peter
8
2019
Detonation and deflagration waves with multistep reaction schemes. Zbl 0814.34028
Gasser, I.; Szmolyan, P.
7
1995
Relative equilibria of tethered satellite systems and their stability for very stiff tethers. Zbl 0998.70020
Krupa, M.; Schagerl, M.; Steindl, A.; Szmolyan, P.; Troger, H.
6
2001
Analysis of a singularly perturbed traveling wave problem. Zbl 0749.34026
Szmolyan, P.
5
1992
A singular perturbation analysis of the transient semiconductor device equations. Zbl 0699.35014
Szmolyan, Peter
4
1989
Persistence of rarefactions under Dafermos regularization: blow-up and an exchange lemma for gain-of-stability turning points. Zbl 1178.35252
Schecter, Stephen; Szmolyan, Peter
4
2009
Graph transform and blow-up in singular perturbations. Zbl 1182.65109
Nipp, Kaspar; Stoffer, Daniel; Szmolyan, Peter
3
2009
Qualitative dynamics of chemical reaction networks: an investigation using partial tropical equilibrations. Zbl 1505.92073
Desoeuvres, Aurélien; Szmolyan, Peter; Radulescu, Ovidiu
3
2022
Singularly perturbed oscillators with exponential nonlinearities. Zbl 1505.34087
Jelbart, S.; Kristiansen, K. U.; Szmolyan, P.; Wechselberger, M.
3
2022
Asymptotic methods for transient semiconductor device equations. Zbl 0704.35006
Szmolyan, Peter
2
1989
Analysis of the Gunn effect. Zbl 0946.35504
Steinrück, H.; Szmolyan, P.
2
1994
Existence of Chapman-Jouguet detonation and deflagration waves. Zbl 1343.35186
Gasser, Ingenuin; Szmolyan, Peter; Wächtler, Johannes
2
2016
Oscillations in a cAMP signalling model for cell aggregation – a geometric analysis. Zbl 1431.34067
Miao, Zhouqian; Popović, Nikola; Szmolyan, Peter
2
2020
Saddle-node bifurcation of viscous profiles. Zbl 1257.35033
Achleitner, Franz; Szmolyan, Peter
2
2012
Geometric analysis of oscillations in the Frzilator model. Zbl 1483.34067
Taghvafard, Hadi; Jardón-Kojakhmetov, Hildeberto; Szmolyan, Peter; Cao, Ming
2
2021
Traveling waves in GaAs semiconductors. Zbl 0850.76017
Szmolyan, Peter
1
1989
Initial transients of solutions of the semiconductor device equations. Zbl 0788.65120
Szmolyan, P.
1
1990
Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem. Zbl 1434.70055
Iuorio, Annalisa; Kuehn, Christian; Szmolyan, Peter
1
2020
A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour. Zbl 1497.34086
Iuorio, Annalisa; Jankowiak, Gaspard; Szmolyan, Peter; Wolfram, Marie-Therese
1
2022
Qualitative dynamics of chemical reaction networks: an investigation using partial tropical equilibrations. Zbl 1505.92073
Desoeuvres, Aurélien; Szmolyan, Peter; Radulescu, Ovidiu
3
2022
Singularly perturbed oscillators with exponential nonlinearities. Zbl 1505.34087
Jelbart, S.; Kristiansen, K. U.; Szmolyan, P.; Wechselberger, M.
3
2022
A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour. Zbl 1497.34086
Iuorio, Annalisa; Jankowiak, Gaspard; Szmolyan, Peter; Wolfram, Marie-Therese
1
2022
Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit. Zbl 1477.34074
Uldall Kristiansen, K.; Szmolyan, P.
9
2021
Geometric analysis of oscillations in the Frzilator model. Zbl 1483.34067
Taghvafard, Hadi; Jardón-Kojakhmetov, Hildeberto; Szmolyan, Peter; Cao, Ming
2
2021
Oscillations in a cAMP signalling model for cell aggregation – a geometric analysis. Zbl 1431.34067
Miao, Zhouqian; Popović, Nikola; Szmolyan, Peter
2
2020
Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem. Zbl 1434.70055
Iuorio, Annalisa; Kuehn, Christian; Szmolyan, Peter
1
2020
Singular perturbation analysis of a regularized MEMS model. Zbl 1458.34103
Iuorio, Annalisa; Popović, Nikola; Szmolyan, Peter
8
2019
Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle. Zbl 1344.34068
Kosiuk, Ilona; Szmolyan, Peter
24
2016
Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations. Zbl 1380.37105
Hayes, Michael G.; Kaper, Tasso J.; Szmolyan, Peter; Wechselberger, Martin
13
2016
Existence of Chapman-Jouguet detonation and deflagration waves. Zbl 1343.35186
Gasser, Ingenuin; Szmolyan, Peter; Wächtler, Johannes
2
2016
Multiscale geometry of the Olsen model and non-classical relaxation oscillations. Zbl 1321.34065
Kuehn, Christian; Szmolyan, Peter
21
2015
Saddle-node bifurcation of viscous profiles. Zbl 1257.35033
Achleitner, Franz; Szmolyan, Peter
2
2012
Scaling in singular perturbation problems: blowing up a relaxation oscillator. Zbl 1243.34066
Kosiuk, Ilona; Szmolyan, Peter
30
2011
Spectral stability of small-amplitude viscous shock waves in several space dimensions. Zbl 1188.35117
Freistühler, Heinrich; Szmolyan, Peter
14
2010
Geometric singular perturbation analysis of an autocatalator model. Zbl 1362.34076
Gucwa, Ilona; Szmolyan, Peter
33
2009
Persistence of rarefactions under Dafermos regularization: blow-up and an exchange lemma for gain-of-stability turning points. Zbl 1178.35252
Schecter, Stephen; Szmolyan, Peter
4
2009
Graph transform and blow-up in singular perturbations. Zbl 1182.65109
Nipp, Kaspar; Stoffer, Daniel; Szmolyan, Peter
3
2009
Asymptotic expansions using blow-up. Zbl 1081.34052
van Gils, S.; Krupa, M.; Szmolyan, P.
21
2005
Geometric singular perturbation analysis of the Yamada model. Zbl 1106.34027
Huber, A.; Szmolyan, P.
9
2005
Relaxation oscillations in \({\mathbb R}^3\). Zbl 1058.34055
Szmolyan, P.; Wechselberger, M.
62
2004
Composite waves in the Dafermos regularization. Zbl 1076.35074
Schecter, Stephen; Szmolyan, Peter
14
2004
A geometric analysis of the Lagerstrom model problem. Zbl 1059.34033
Popović, Nikola; Szmolyan, Peter
10
2004
Rigorous asymptotic expansions for Lagerstrom’s model equation – a geometric approach. Zbl 1082.34045
Popović, Nikola; Szmolyan, Peter
8
2004
Spectral stability of small shock waves. Zbl 1018.35010
Freistühler, H.; Szmolyan, P.
30
2002
Extending geometric singular perturbation theory to nonhyperbolic points – fold and canard points in two dimensions. Zbl 1002.34046
Krupa, M.; Szmolyan, P.
245
2001
Relaxation oscillation and canard explosion. Zbl 0994.34032
Krupa, M.; Szmolyan, P.
210
2001
Canards in \(\mathbb{R}^3\). Zbl 1007.34057
Szmolyan, Peter; Wechselberger, Martin
149
2001
Extending slow manifolds near transcritical and pitchfork singularities. Zbl 0998.34039
Krupa, M.; Szmolyan, P.
71
2001
Geometric analysis of the singularly perturbed planar fold. Zbl 1013.34057
Krupa, M.; Szmolyan, P.
19
2001
Multiple time scales and canards in a chemical oscillator. Zbl 1013.34044
Milik, Alexandra; Szmolyan, Peter
17
2001
Relative equilibria of tethered satellite systems and their stability for very stiff tethers. Zbl 0998.70020
Krupa, M.; Schagerl, M.; Steindl, A.; Szmolyan, P.; Troger, H.
6
2001
Bifurcation of traveling waves in extrinsic semiconductors. Zbl 0960.34031
Katzengruber, B.; Krupa, M.; Szmolyan, P.
11
2000
Geometry of mixed-mode oscillations in the 3-D autocatalator. Zbl 0933.92036
Milik, Alexandra; Szmolyan, Peter; Löffelmann, Helwig; Gröller, Eduard
34
1998
Fast and slow waves in the FitzHugh-Nagumo equation. Zbl 0898.34050
Krupa, Martin; Sandstede, Björn; Szmolyan, Peter
62
1997
Existence and bifurcation of viscous profiles for all intermediate magnetohydrodynamic shock waves. Zbl 0817.34028
Freistühler, H.; Szmolyan, P.
36
1995
Detonation and deflagration waves with multistep reaction schemes. Zbl 0814.34028
Gasser, I.; Szmolyan, P.
7
1995
Analysis of the Gunn effect. Zbl 0946.35504
Steinrück, H.; Szmolyan, P.
2
1994
A geometric singular perturbation analysis of detonation and deflagration waves. Zbl 0783.76099
Gasser, I.; Szmolyan, P.
24
1993
Analysis of a singularly perturbed traveling wave problem. Zbl 0749.34026
Szmolyan, P.
5
1992
Transversal heteroclinic and homoclinic orbits in singular perturbation problems. Zbl 0734.34038
Szmolyan, P.
66
1991
Initial transients of solutions of the semiconductor device equations. Zbl 0788.65120
Szmolyan, P.
1
1990
A system of convection-diffusion equations with small diffusion coefficient arising in semiconductor physics. Zbl 0709.35058
Markowich, Peter A.; Szmolyan, Peter
17
1989
A singular perturbation analysis of the transient semiconductor device equations. Zbl 0699.35014
Szmolyan, Peter
4
1989
Asymptotic methods for transient semiconductor device equations. Zbl 0704.35006
Szmolyan, Peter
2
1989
Traveling waves in GaAs semiconductors. Zbl 0850.76017
Szmolyan, Peter
1
1989
all top 5

Cited by 819 Authors

32 Wechselberger, Martin
31 Kühn, Christian
28 Uldall Kristiansen, K.
28 Zumbrun, Kevin R.
26 Szmolyan, Peter
23 Desroches, Mathieu
21 De Maesschalck, Peter
16 Huzak, Renato
16 Krupa, Martin
15 Popović, Nikola
13 Kaper, Tasso J.
13 Vo, Theodore
12 Jardón-Kojakhmetov, Hildeberto
11 Carter, Paul M.
10 Dumortier, Freddy
10 Freistühler, Heinrich
9 Da Silva, Paulo Ricardo
9 Li, Ji
9 Shen, Jianhe
8 Humpherys, Jeffrey
8 Krauskopf, Bernd
8 Liu, Qian
8 Llibre, Jaume
8 Lyng, Gregory Daniel
8 Osinga, Hinke Maria
8 Rubin, Jonathan E.
8 Scheel, Arnd
8 Zhou, Yuqian
7 Brøns, Morten
7 Hogan, S. John
7 Jelbart, Samuel
7 Rotstein, Horacio G.
7 Schecter, Stephen
6 Algaba, Antonio
6 Bertram, Richard
6 Chung, Kwok-Wai
6 Engel, Maximilian
6 Fernández-García, Soledad
6 Iuorio, Annalisa
6 Kirk, Vivien
6 Liu, Weishi
6 Métivier, Guy
6 Qin, Bo-Wei
6 Rodrigues, Serafim
6 Rodríguez-Luis, Alejandro J.
6 Sandstede, Björn
6 Steindl, Alois
6 Williams, Mark
6 Zhang, Xiang
5 Barker, Blake
5 Ersöz, Elif Köksal
5 Ginoux, Jean-Marc
5 Han, Maoan
5 Hupkes, Hermen Jan
5 Marangell, Robert
5 Teixeira, Marco Antonio
5 van Heijster, Peter
5 Wang, Dehua
4 Ashwin, Peter
4 Banasiak, Jacek
4 Banerjee, Malay
4 Bates, Peter W.
4 Cardin, Pedro Toniol
4 Doelman, Arjen
4 Guès, Olivier
4 Holzer, Matt
4 Hsu, Cheng-Hsiung
4 Jones, Christopher K. R. T.
4 Lu, Kening
4 Medvedev, Georgi S.
4 Rohde, Christian
4 Roussarie, Robert
4 Sadhu, Susmita
4 Schouten-Straatman, Willem M.
4 Sensi, Mattia
4 Sneyd, James
4 Sourdis, Christos
4 Tabak, Joël
4 Van Vleck, Erik S.
4 Wieczorek, Sebastian M.
4 Yanchuk, Sergiĭ Volodymyrovych
4 Yin, Haiyan
4 Zhang, Weinian
3 Abdelkawy, Mohamed A.
3 Avitabile, Daniele
3 Battelli, Flaviano
3 Berglund, Nils
3 Bi, Qinsheng
3 Bossolini, Elena
3 Broer, Henk W.
3 Chen, Shuang
3 Chowdhury, Pranali Roy
3 Du, Zengji
3 Duan, Jinqiao
3 Eilertsen, Justin S.
3 Gentz, Barbara
3 Hong, John Meng-Kai
3 Howard, Peter
3 Hu, Xianpeng
3 Jeffrey, Mike R.
...and 719 more Authors
all top 5

Cited in 129 Serials

73 Journal of Differential Equations
52 Physica D
46 SIAM Journal on Applied Dynamical Systems
24 Journal of Dynamics and Differential Equations
24 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
18 Journal of Mathematical Analysis and Applications
18 Journal of Nonlinear Science
18 Chaos
16 Archive for Rational Mechanics and Analysis
15 Nonlinearity
14 Journal of Mathematical Biology
13 Nonlinear Dynamics
13 Discrete and Continuous Dynamical Systems. Series B
10 Applied Mathematics and Computation
10 Nonlinear Analysis. Real World Applications
10 Dynamical Systems
10 The Journal of Mathematical Neuroscience
9 Chaos, Solitons and Fractals
9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
9 Communications in Nonlinear Science and Numerical Simulation
8 Mathematical Biosciences
8 SIAM Journal on Mathematical Analysis
8 Qualitative Theory of Dynamical Systems
7 Transactions of the American Mathematical Society
7 Discrete and Continuous Dynamical Systems
7 Journal of Dynamical and Control Systems
7 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
6 Bulletin of Mathematical Biology
6 SIAM Journal on Applied Mathematics
6 Mathematical Modelling of Natural Phenomena
5 Biological Cybernetics
5 ZAMP. Zeitschrift für angewandte Mathematik und Physik
5 Quarterly of Applied Mathematics
5 Applied Mathematics Letters
5 Journal of Computational Neuroscience
5 Mathematical Biosciences and Engineering
4 Communications in Mathematical Physics
4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
4 Discrete and Continuous Dynamical Systems. Series S
4 Journal of Theoretical Biology
3 Mathematical Methods in the Applied Sciences
3 Mathematical and Computer Modelling
3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
3 Applied Mathematical Modelling
3 Communications in Partial Differential Equations
3 SIAM Review
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Communications on Pure and Applied Analysis
3 Nonlinear Analysis. Theory, Methods & Applications
3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
2 Applicable Analysis
2 Journal of Computational Physics
2 Journal of Mathematical Physics
2 Transport Theory and Statistical Physics
2 Mathematics of Computation
2 Advances in Mathematics
2 BIT
2 Transactions of the Moscow Mathematical Society
2 Circuits, Systems, and Signal Processing
2 Chinese Annals of Mathematics. Series B
2 Acta Applicandae Mathematicae
2 Acta Mathematicae Applicatae Sinica. English Series
2 European Journal of Applied Mathematics
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Indagationes Mathematicae. New Series
2 Journal of Mathematical Sciences (New York)
2 Computational and Applied Mathematics
2 Mathematical Problems in Engineering
2 Mathematical Population Studies
2 Discrete Dynamics in Nature and Society
2 New Journal of Physics
2 Combustion Theory and Modelling
2 Journal of Hyperbolic Differential Equations
2 Science China. Mathematics
1 Bulletin of the Australian Mathematical Society
1 Computers & Mathematics with Applications
1 Computer Methods in Applied Mechanics and Engineering
1 Communications on Pure and Applied Mathematics
1 Israel Journal of Mathematics
1 Journal of Engineering Mathematics
1 Journal of Fluid Mechanics
1 Physics Reports
1 Prikladnaya Matematika i Mekhanika
1 Annales de l’Institut Fourier
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Archiv der Mathematik
1 Automatica
1 Journal of Computational and Applied Mathematics
1 Journal of Functional Analysis
1 Michigan Mathematical Journal
1 Proceedings of the American Mathematical Society
1 Theoretical Computer Science
1 Theoretical Population Biology
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Numerical Methods for Partial Differential Equations
1 Journal of Economic Dynamics & Control
1 Journal of the American Mathematical Society
1 The Annals of Applied Probability
1 International Journal of Computer Mathematics
...and 29 more Serials
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Cited in 38 Fields

416 Ordinary differential equations (34-XX)
216 Partial differential equations (35-XX)
210 Biology and other natural sciences (92-XX)
177 Dynamical systems and ergodic theory (37-XX)
88 Fluid mechanics (76-XX)
41 Mechanics of particles and systems (70-XX)
37 Numerical analysis (65-XX)
15 Mechanics of deformable solids (74-XX)
15 Classical thermodynamics, heat transfer (80-XX)
14 Statistical mechanics, structure of matter (82-XX)
11 Optics, electromagnetic theory (78-XX)
9 Geophysics (86-XX)
9 Information and communication theory, circuits (94-XX)
8 Probability theory and stochastic processes (60-XX)
7 Systems theory; control (93-XX)
6 Global analysis, analysis on manifolds (58-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Difference and functional equations (39-XX)
4 Integral equations (45-XX)
3 Measure and integration (28-XX)
3 Differential geometry (53-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Real functions (26-XX)
2 Approximations and expansions (41-XX)
2 Functional analysis (46-XX)
2 Operator theory (47-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
2 Computer science (68-XX)
2 Astronomy and astrophysics (85-XX)
1 Combinatorics (05-XX)
1 Number theory (11-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Special functions (33-XX)
1 General topology (54-XX)
1 Statistics (62-XX)
1 Quantum theory (81-XX)
1 Relativity and gravitational theory (83-XX)
1 Operations research, mathematical programming (90-XX)

Citations by Year