×

zbMATH — the first resource for mathematics

Zumbrun, Kevin R.

Compute Distance To:
Author ID: zumbrun.kevin-r Recent zbMATH articles by "Zumbrun, Kevin R."
Published as: Zumbrun, Kevin; Zumbrun, K.; Zumbrun, Kevin R.; Zumbrun, Keven
Homepage: http://pages.iu.edu/~kzumbrun
External Links: MGP · ResearchGate
Documents Indexed: 174 Publications since 1992, including 1 Book
all top 5

Serials

26 Archive for Rational Mechanics and Analysis
12 Journal of Differential Equations
12 Physica D
11 SIAM Journal on Mathematical Analysis
10 Communications in Mathematical Physics
6 Indiana University Mathematics Journal
6 Quarterly of Applied Mathematics
5 Communications on Pure and Applied Mathematics
4 ZAMP. Zeitschrift für angewandte Mathematik und Physik
4 Proceedings of the American Mathematical Society
4 Zeitschrift für Analysis und ihre Anwendungen
4 Journal de Mathématiques Pures et Appliquées. Neuvième Série
4 Discrete and Continuous Dynamical Systems
3 Transactions of the American Mathematical Society
3 SIAM Journal on Applied Mathematics
3 Matemática Contemporânea
3 Journal of Hyperbolic Differential Equations
3 Kinetic and Related Models
2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Applied Mathematics Letters
2 Communications in Partial Differential Equations
2 Journal of Nonlinear Science
2 Séminaire Équations aux Dérivées Partielles
2 Methods and Applications of Analysis
2 SIAM Journal on Applied Dynamical Systems
1 Journal of Mathematical Analysis and Applications
1 Journal of Mathematical Biology
1 Nonlinearity
1 Duke Mathematical Journal
1 Inventiones Mathematicae
1 Journal für die Reine und Angewandte Mathematik
1 Memoirs of the American Mathematical Society
1 Numerische Mathematik
1 SIAM Journal on Numerical Analysis
1 Studies in Applied Mathematics
1 Statistics & Probability Letters
1 Journal of the American Mathematical Society
1 European Journal of Applied Mathematics
1 Differential and Integral Equations
1 Mathematica Bohemica
1 The Annals of Applied Probability
1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
1 Journal of Dynamics and Differential Equations
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Communications in Analysis and Geometry
1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
1 Acta Mathematica Scientia. Series B. (English Edition)

Publications by Year

Citations contained in zbMATH Open

157 Publications have been cited 2,699 times in 868 Documents Cited by Year
Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow. Zbl 0842.35076
Hoff, David; Zumbrun, Kevin
140
1995
Pointwise semigroup methods and stability of viscous shock waves. Zbl 0928.35018
Zumbrun, Kevin; Howard, Peter
103
1998
Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves. Zbl 0882.76074
Hoff, David; Zumbrun, Kevin
89
1997
The gap lemma and geometric criteria for instability of viscous shock profiles. Zbl 0933.35136
Gardner, Robert A.; Zumbrun, Kevin
71
1998
Multidimensional stability of planar viscous shock waves. Zbl 0989.35089
Zumbrun, Kevin
62
2001
Pointwise Green function bounds for shock profiles of systems with real viscosity. Zbl 1035.35074
Mascia, Corrado; Zumbrun, Kevin
61
2003
Stability of large-amplitude shock waves of compressible Navier-Stokes equations. With an appendix by Helge Kristian Jenssen and Gregory Lyng. Zbl 1222.35156
Zumbrun, Keven
60
2004
Stability of large-amplitude viscous shock profiles of hyperbolic-parabolic systems. Zbl 1058.35160
Mascia, Corrado; Zumbrun, Kevin
56
2004
Connectivity of phase boundaries in strictly convex domains. Zbl 0911.49025
Sternberg, Peter; Zumbrun, Kevin
55
1998
An efficient shooting algorithm for Evans function calculations in large systems. Zbl 1101.65082
Humpherys, Jeffrey; Zumbrun, Kevin
51
2006
Viscous and inviscid stability of multidimensional planar shock fronts. Zbl 0944.76027
Zumbrun, K.; Serre, D.
49
1999
An Evans function approach to spectral stability of small-amplitude shock profiles. Zbl 1058.35164
Plaza, Ramon; Zumbrun, Kevin
47
2004
A Poincaré inequality with applications to volume-constrained area-minimizing surfaces. Zbl 0967.53006
Sternberg, Peter; Zumbrun, Kevin
44
1998
Analytically varying eigenvectors and the stability of viscous shock waves. Zbl 1044.35057
Brin, Leon Q.; Zumbrun, Kevin
42
2002
Pointwise Green’s function bounds and stability of relaxation shocks. Zbl 1036.35135
Mascia, Corrado; Zumbrun, Kevin
40
2002
Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1074.35066
Métivier, Guy; Zumbrun, Kevin
40
2005
Stability of isentropic Navier-Stokes shocks in the high-Mach number limit. Zbl 1195.35244
Humpherys, Jeffrey; Lafitte, Olivier; Zumbrun, Kevin
31
2010
Stability of viscous shocks in isentropic gas dynamics. Zbl 1171.35071
Barker, Blake; Humpherys, Jeffrey; Rudd, Keith; Zumbrun, Kevin
31
2008
Hyperbolic boundary value problems for symmetric systems with variable multiplicities. Zbl 1073.35155
Métivier, Guy; Zumbrun, Kevin
31
2005
Spectral stability of ideal-gas shock layers. Zbl 1422.76122
Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
30
2009
Stability of small-amplitude shock profiles of symmetric hyperbolic-parabolic systems. Zbl 1060.35111
Mascia, C.; Zumbrun, K.
30
2004
Stability of periodic solutions of conservation laws with viscosity: analysis of the Evans function. Zbl 1074.35006
Oh, M.; Zumbrun, K.
30
2003
Boundary layer stability in real vanishing viscosity limit. Zbl 0988.35028
Serre, Denis; Zumbrun, Kevin
29
2001
Stability of rarefaction waves in viscous media. Zbl 0861.35037
Szepessy, Anders; Zumbrun, Kevin
28
1996
Asymptotic behavior of multidimensional scalar viscous shock fronts. Zbl 0967.76049
Hoff, David; Zumbrun, Kevin
28
2000
Planar stability criteria for viscous shock waves of systems with real viscosity. Zbl 1138.35061
Zumbrun, Kevin
28
2007
Existence and stability of multidimensional shock fronts in the vanishing viscosity limit. Zbl 1072.35122
Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
27
2005
Spectral stability of small-amplitude shock profiles for dissipative symmetric hyperbolic-parabolic systems. Zbl 1006.35065
Humpherys, J.; Zumbrun, Kevin
27
2002
Stability of undercompressive shock profiles. Zbl 1102.35069
Howard, Peter; Zumbrun, Kevin
27
2006
Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations. Zbl 1304.35192
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
27
2014
Alternate Evans functions and viscous shock waves. Zbl 0985.34075
Benzoni-Gavage, Sylvie; Serre, Denis; Zumbrun, Kevin
26
2001
Stability of large-amplitude shock profiles of general relaxation systems. Zbl 1100.35069
Mascia, Corrado; Zumbrun, Kevin
26
2005
Efficient computation of analytic bases in Evans function analysis of large systems. Zbl 1104.65081
Humpherys, Jeffrey; Sandstede, Björn; Zumbrun, Kevin
26
2006
Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation. Zbl 1304.35184
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
26
2013
Galloping instability of viscous shock waves. Zbl 1143.76439
Texier, Benjamin; Zumbrun, Kevin
25
2008
On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint. Zbl 0930.49024
Sternberg, Peter; Zumbrun, Kevin
24
1999
Navier-Stokes regularization of multidimensional Euler shocks. Zbl 1173.35082
Guès, C. M. I. Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
24
2006
Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case. Zbl 1198.35027
Johnson, Mathew A.; Zumbrun, Kevin
23
2010
Stability of periodic solutions of conservation laws with viscosity: Pointwise bounds on the Green function. Zbl 1031.35022
Oh, M.; Zumbrun, K.
23
2003
Hopf bifurcation of viscous shock waves in compressible gas dynamics and MHD. Zbl 1155.76037
Texier, Benjamin; Zumbrun, Kevin
23
2008
Existence and stability of noncharacteristic boundary layers for the compressible Navier-Stokes and viscous MHD equations. Zbl 1217.35136
Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
22
2010
Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction-diffusion equations. Zbl 1246.35034
Johnson, Mathew A.; Zumbrun, Kevin
21
2011
Relative Poincaré-Hopf bifurcation and galloping instability of traveling waves. Zbl 1370.37136
Texier, Benjamin; Zumbrun, Kevin
20
2005
One-dimensional stability of parallel shock layers in isentropic magnetohydrodynamics. Zbl 1402.76051
Barker, Blake; Humpherys, Jeffrey; Zumbrun, Kevin
19
2010
One-dimensional stability of viscous strong detonation waves. Zbl 1067.76041
Lyng, Gregory; Zumbrun, Kevin
19
2004
Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions. Zbl 1217.35138
Texier, Benjamin; Zumbrun, Kevin
18
2011
Nonlinear stability of time-periodic viscous shocks. Zbl 1221.35054
Beck, Margaret; Sandstede, Björn; Zumbrun, Kevin
18
2010
Existence of relaxation shock profiles for hyperbolic conservation laws. Zbl 0959.35116
Yong, Wen-An; Zumbrun, Kevin
18
2000
Dynamical stability of phase transitions in the \(p\)-system with viscosity-capillarity. Zbl 0973.35183
Zumbrun, Kevin
18
2000
Stability of compressive and undercompressive thin film travelling waves. Zbl 1028.76012
Bertozzi, Andrea L.; Münch, Andreas; Shearer, Michael; Zumbrun, Kevin
18
2001
Refined wave-tracking and nonlinear stability of viscous Lax shocks. Zbl 1007.35048
Zumbrun, Kevin
18
2000
Nonlinear stability of an undercompressive shock for complex Burgers equation. Zbl 0821.35123
Liu, Tai-Ping; Zumbrun, Kevin
17
1995
On a nonlocal dispersive equation modeling particle suspensions. Zbl 1020.35058
Zumbrun, Kevin
17
1999
A stability index for detonation waves in Majda’s model for reacting flow. Zbl 1061.35018
Lyng, Gregory; Zumbrun, Kevin
17
2004
Capillary instability in models for three-phase flow. Zbl 1015.35068
Azevedo, A. V.; Marchesin, D.; Plohr, B.; Zumbrun, K.
17
2002
Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation. Zbl 1270.35106
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
17
2013
Nonlinear stability of viscous roll waves. Zbl 1240.35037
Johnson, Mathew A.; Zumbrun, Kevin; Noble, Pascal
17
2011
On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions. Zbl 1211.37087
Johnson, Mathew A.; Zumbrun, Kevin; Bronski, Jared C.
16
2010
Pointwise Green function bounds and stability of combustion waves. Zbl 1116.80017
Lyng, Gregory; Raoofi, Mohammadreza; Texier, Benjamin; Zumbrun, Kevin
16
2007
Transverse instability of periodic traveling waves in the generalized Kadomtsev-Petviashvili equation. Zbl 1233.35025
Johnson, Mathew A.; Zumbrun, Kevin
16
2010
On nonlinear stability of general undercompressive viscous shock waves. Zbl 0840.76028
Liu, Tai-Ping; Zumbrun, Kevin
16
1995
Pointwise estimates and stability for dispersive-diffusive shock waves. Zbl 0977.35080
Howard, Peter; Zumbrun, Kevin
16
2000
Multidimensional viscous shocks. I: Degenerate symmetrizers and long time stability. Zbl 1058.35163
Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
16
2005
Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability. Zbl 1276.35031
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
16
2013
Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves. Zbl 1161.47058
Gesztesy, Fritz; Latushkin, Yuri; Zumbrun, Kevin
15
2008
Stability of detonation profiles in the ZND limit. Zbl 1233.35030
Zumbrun, Kevin
15
2011
Pointwise Green’s function bounds for multidimensional scalar viscous shock fronts. Zbl 1028.35108
Hoff, David; Zumbrun, Kevin
15
2002
Multidimensional stability of large-amplitude Navier-Stokes shocks. Zbl 1386.35326
Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
15
2017
Stability of radiative shock profiles for hyperbolic-elliptic coupled systems. Zbl 1195.37045
Nguyen, Toan; Plaza, Ramón G.; Zumbrun, Kevin
14
2010
Spectral stability of noncharacteristic isentropic Navier-Stokes boundary layers. Zbl 1169.76051
Costanzino, Nicola; Humpherys, Jeffrey; Nguyen, Toan; Zumbrun, Kevin
14
2009
Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions. Zbl 1197.35075
Oh, Myunghyun; Zumbrun, Kevin
13
2010
Rigorous justification of the Whitham modulation equations for the generalized Korteweg-de Vries equation. Zbl 1196.35184
Johnson, M. A.; Zumbrun, K.
13
2010
Nonlinear stability of periodic traveling-wave solutions of viscous conservation laws in dimensions one and two. Zbl 1221.35055
Johnson, Mathew A.; Zumbrun, Kevin
13
2011
Multidimensional viscous shocks. II: The small viscosity limit. Zbl 1073.35162
Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
13
2004
Stability of undercompressive viscous shock profiles of hyperbolic-parabolic systems. Zbl 1170.35019
Raoofi, Mohammadreza; Zumbrun, Kevin
13
2009
Existence and stability of viscoelastic shock profiles. Zbl 1233.35023
Barker, Blake; Lewicka, Marta; Zumbrun, Kevin
12
2011
Viscous hyperstabilization of detonation waves in one space dimension. Zbl 1320.35271
Barker, Blake; Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
12
2015
The resistive state in a superconducting wire: Bifurcation from the normal state. Zbl 1187.82150
Rubinstein, Jacob; Sternberg, Peter; Zumbrun, Kevin
11
2010
Instantaneous shock location and one-dimensional nonlinear stability of viscous shock waves. Zbl 1221.35059
Zumbrun, Kevin
11
2011
Low-frequency stability analysis of periodic traveling-wave solutions of viscous conservation laws in several dimensions. Zbl 1099.35014
Oh, Myunghyun; Zumbrun, Kevin
11
2006
Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit. Zbl 1310.35035
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
11
2015
Existence and stability of viscous shock profiles for 2-D isentropic MHD with infinite electrical resistivity. Zbl 1240.35033
Barker, Blake; Lafitte, Olivier; Zumbrun, Kevin
10
2010
Scattering behavior of transitional shock waves. Zbl 0854.35070
Zumbrun, Kevin R.; Plohr, Bradley J.; Marchesin, Dan
10
1992
Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems. Zbl 1102.35332
Métivier, G.; Zumbrun, K.
10
2004
Sharp pointwise bounds for perturbed viscous shock waves. Zbl 1103.35073
Howard, Peter; Raoofi, Mohammadreza; Zumbrun, Kevin
10
2006
Stability of periodic Kuramoto-Sivashinsky waves. Zbl 1238.35094
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
10
2012
A local greedy algorithm and higher-order extensions for global numerical continuation of analytically varying subspaces. Zbl 1195.65105
Zumbrun, Kevin
9
2010
Nonuniqueness of solutions of Riemann problems. Zbl 0880.35068
Azevedo, Arthur V.; Marchesin, Dan; Plohr, Bradley J.; Zumbrun, Kevin
9
1996
The Evans function and stability criteria for degenerate viscous shock waves. Zbl 1058.35033
Howard, Peter; Zumbrun, Kevin
9
2004
Viscous boundary value problems for symmetric systems with variable multiplicities. Zbl 1138.35052
Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
9
2008
Efficient numerical stability analysis of detonation waves in ZND. Zbl 1390.76090
Humpherys, Jeffrey; Zumbrun, Kevin
9
2012
Metastability of solitary roll wave solutions of the St. Venant equations with viscosity. Zbl 1223.37109
Barker, Blake; Johnson, Mathew A.; Rodrigues, L. Miguel; Zumbrun, Kevin
9
2011
Convergence of Hill’s method for nonselfadjoint operators. Zbl 1246.65134
Johnson, Mathew A.; Zumbrun, Kevin
9
2012
Stability and dynamics of viscous shock waves. Zbl 1258.35028
Zumbrun, Kevin
9
2011
High-frequency asymptotics and one-dimensional stability of Zel’dovich-von Neumann-Döring detonations in the small-heat release and high-overdrive limits. Zbl 1318.76022
Zumbrun, Kevin
8
2012
Stability of scalar radiative shock profiles. Zbl 1218.35031
Lattanzio, Corrado; Mascia, Corrado; Nguyen, Toan; Plaza, Ramón G.; Zumbrun, Kevin
8
2009
Long-time stability of large-amplitude noncharacteristic boundary layers for hyperbolic-parabolic systems. Zbl 1188.35021
Nguyen, Toan; Zumbrun, Kevin
8
2009
Bifurcation of nonclassical viscous shock profiles from the constant state. Zbl 0954.35111
Azevedo, A. V.; Marchesin, D.; Plohr, B.; Zumbrun, K.
8
1999
Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit. Zbl 1373.35040
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
8
2017
Pointwise Green function bounds and long-time stability of large-amplitude noncharacteristic boundary layers. Zbl 1180.35145
Yarahmadian, Shantia; Zumbrun, Kevin
7
2009
Stability of hydraulic shock profiles. Zbl 1430.35157
Yang, Zhao; Zumbrun, Kevin
2
2020
Spectral stability of inviscid roll waves. Zbl 1455.35013
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Yang, Zhao; Zumbrun, Kevin
5
2019
Convergence as period goes to infinity of spectra of periodic traveling waves toward essential spectra of a homoclinic limit. Zbl 1445.35108
Yang, Zhao; Zumbrun, Kevin
2
2019
Existence and stability of steady compressible Navier-Stokes solutions on a finite interval with noncharacteristic boundary conditions. Zbl 1451.76106
Melinand, Benjamin; Zumbrun, Kevin
1
2019
Diffusive stability of spatially periodic solutions of the Brusselator model. Zbl 1390.35127
Sukhtayev, Alim; Zumbrun, Kevin; Jung, Soyeun; Venkatraman, Raghavendra
2
2018
Invariant manifolds for a class of degenerate evolution equations and structure of kinetic shock layers. Zbl 1405.37087
Zumbrun, Kevin
2
2018
A singular local minimizer for the volume-constrained minimal surface problem in a nonconvex domain. Zbl 1401.49055
Sternberg, Peter; Zumbrun, Kevin
2
2018
Balanced flux formulations for multidimensional Evans-function computations for viscous shocks. Zbl 1398.35160
Barker, Blake; Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
2
2018
Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks. Zbl 1392.35043
Pogan, Alin; Zumbrun, Kevin
2
2018
Multidimensional stability of large-amplitude Navier-Stokes shocks. Zbl 1386.35326
Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
15
2017
Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit. Zbl 1373.35040
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
8
2017
\(L^\infty\) resolvent bounds for steady Boltzmann’s equation. Zbl 1358.35084
Zumbrun, Kevin
4
2017
On nonlinear stabilization of linearly unstable maps. Zbl 1386.37023
Gallay, Thierry; Texier, Benjamin; Zumbrun, Kevin
1
2017
Recent results on stability of planar detonations. Zbl 1366.76033
Zumbrun, Kevin
1
2017
Numerical proof of stability of viscous shock profiles. Zbl 1356.35170
Barker, Blake; Zumbrun, Kevin
6
2016
Periodic-coefficient damping estimates, and stability of large-amplitude roll waves in inclined thin film flow. Zbl 1341.35128
Rodrigues, L. Miguel; Zumbrun, Kevin
5
2016
Pointwise nonlinear stability of nonlocalized modulated periodic reaction-diffusion waves. Zbl 1353.35053
Jung, Soyeun; Zumbrun, Kevin
4
2016
Block-diagonalization of ODEs in the semiclassical limit and \(C^\omega\) versus \(C^\infty\) stationary phase. Zbl 1347.34094
Lafitte, Olivier; Williams, Mark; Zumbrun, Kevin
2
2016
Viscous hyperstabilization of detonation waves in one space dimension. Zbl 1320.35271
Barker, Blake; Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
12
2015
Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit. Zbl 1310.35035
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
11
2015
Convex entropy, Hopf bifurcation, and viscous and inviscid shock stability. Zbl 1329.35240
Barker, Blake; Freistühler, Heinrich; Zumbrun, Kevin
7
2015
Stability of viscous weak detonation waves for Majda’s model. Zbl 1326.35199
Hendricks, Jeffrey; Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
6
2015
\(O(2)\) Hopf bifurcation of viscous shock waves in a channel. Zbl 1364.37109
Pogan, Alin; Yao, Jinghua; Zumbrun, Kevin
6
2015
Entropy criteria and stability of extreme shocks: a remark on a paper of Leger and Vasseur. Zbl 1332.35221
Texier, Benjamin; Zumbrun, Kevin
5
2015
High-frequency stability of detonations and turning points at infinity. Zbl 1321.80004
Lafitte, Olivier; Williams, Mark; Zumbrun, Kevin
4
2015
Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations. Zbl 1304.35192
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
27
2014
Nonlinear stability of source defects in the complex Ginzburg-Landau equation. Zbl 1291.35374
Beck, Margaret; Nguyen, Toan T.; Sandstede, Björn; Zumbrun, Kevin
6
2014
Viscous boundary layers in hyperbolic-parabolic systems with Neumann boundary conditions. (Couches limites visqueuses pour des systèmes hyperboliques-paraboliques avec condition aux limites de Neumann.) Zbl 1295.35035
Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
1
2014
Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation. Zbl 1304.35184
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
26
2013
Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation. Zbl 1270.35106
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
17
2013
Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability. Zbl 1276.35031
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
16
2013
Quasi-gradient systems, modulational dichotomies, and stability of spatially periodic patterns. Zbl 1289.35030
Pogan, Alin; Scheel, Arnd; Zumbrun, Kevin
5
2013
Stability of periodic Kuramoto-Sivashinsky waves. Zbl 1238.35094
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
10
2012
Efficient numerical stability analysis of detonation waves in ZND. Zbl 1390.76090
Humpherys, Jeffrey; Zumbrun, Kevin
9
2012
Convergence of Hill’s method for nonselfadjoint operators. Zbl 1246.65134
Johnson, Mathew A.; Zumbrun, Kevin
9
2012
High-frequency asymptotics and one-dimensional stability of Zel’dovich-von Neumann-Döring detonations in the small-heat release and high-overdrive limits. Zbl 1318.76022
Zumbrun, Kevin
8
2012
The Erpenbeck high frequency instability theorem for Zeldovitch-von Neumann-Döring detonations. Zbl 1427.76081
Lafitte, Olivier; Williams, Mark; Zumbrun, Kevin
6
2012
Towards nonlinear stability of sources via a modified Burgers equation. Zbl 1236.35086
Beck, Margaret; Nguyen, Toan; Sandstede, Björn; Zumbrun, Kevin
3
2012
2-modified characteristic Fredholm determinants, Hill’s method, and the periodic Evans function of Gardner. Zbl 1264.34171
Zumbrun, Kevin
3
2012
Existence of quasilinear relaxation shock profiles in systems with characteristic velocities. Zbl 1278.34027
Métivier, Guy; Texier, Benjamin; Zumbrun, Kevin
1
2012
Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction-diffusion equations. Zbl 1246.35034
Johnson, Mathew A.; Zumbrun, Kevin
21
2011
Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions. Zbl 1217.35138
Texier, Benjamin; Zumbrun, Kevin
18
2011
Nonlinear stability of viscous roll waves. Zbl 1240.35037
Johnson, Mathew A.; Zumbrun, Kevin; Noble, Pascal
17
2011
Stability of detonation profiles in the ZND limit. Zbl 1233.35030
Zumbrun, Kevin
15
2011
Nonlinear stability of periodic traveling-wave solutions of viscous conservation laws in dimensions one and two. Zbl 1221.35055
Johnson, Mathew A.; Zumbrun, Kevin
13
2011
Existence and stability of viscoelastic shock profiles. Zbl 1233.35023
Barker, Blake; Lewicka, Marta; Zumbrun, Kevin
12
2011
Instantaneous shock location and one-dimensional nonlinear stability of viscous shock waves. Zbl 1221.35059
Zumbrun, Kevin
11
2011
Metastability of solitary roll wave solutions of the St. Venant equations with viscosity. Zbl 1223.37109
Barker, Blake; Johnson, Mathew A.; Rodrigues, L. Miguel; Zumbrun, Kevin
9
2011
Stability and dynamics of viscous shock waves. Zbl 1258.35028
Zumbrun, Kevin
9
2011
Nash-Moser iteration and singular perturbations. Zbl 1237.47066
Texier, Benjamin; Zumbrun, Kevin
7
2011
Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation. Zbl 1230.92019
Yarahmadian, Shantia; Barker, Blake; Zumbrun, Kevin; Shaw, Sidney L.
3
2011
Stability of isentropic Navier-Stokes shocks in the high-Mach number limit. Zbl 1195.35244
Humpherys, Jeffrey; Lafitte, Olivier; Zumbrun, Kevin
31
2010
Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case. Zbl 1198.35027
Johnson, Mathew A.; Zumbrun, Kevin
23
2010
Existence and stability of noncharacteristic boundary layers for the compressible Navier-Stokes and viscous MHD equations. Zbl 1217.35136
Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
22
2010
One-dimensional stability of parallel shock layers in isentropic magnetohydrodynamics. Zbl 1402.76051
Barker, Blake; Humpherys, Jeffrey; Zumbrun, Kevin
19
2010
Nonlinear stability of time-periodic viscous shocks. Zbl 1221.35054
Beck, Margaret; Sandstede, Björn; Zumbrun, Kevin
18
2010
On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions. Zbl 1211.37087
Johnson, Mathew A.; Zumbrun, Kevin; Bronski, Jared C.
16
2010
Transverse instability of periodic traveling waves in the generalized Kadomtsev-Petviashvili equation. Zbl 1233.35025
Johnson, Mathew A.; Zumbrun, Kevin
16
2010
Stability of radiative shock profiles for hyperbolic-elliptic coupled systems. Zbl 1195.37045
Nguyen, Toan; Plaza, Ramón G.; Zumbrun, Kevin
14
2010
Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions. Zbl 1197.35075
Oh, Myunghyun; Zumbrun, Kevin
13
2010
Rigorous justification of the Whitham modulation equations for the generalized Korteweg-de Vries equation. Zbl 1196.35184
Johnson, M. A.; Zumbrun, K.
13
2010
The resistive state in a superconducting wire: Bifurcation from the normal state. Zbl 1187.82150
Rubinstein, Jacob; Sternberg, Peter; Zumbrun, Kevin
11
2010
Existence and stability of viscous shock profiles for 2-D isentropic MHD with infinite electrical resistivity. Zbl 1240.35033
Barker, Blake; Lafitte, Olivier; Zumbrun, Kevin
10
2010
A local greedy algorithm and higher-order extensions for global numerical continuation of analytically varying subspaces. Zbl 1195.65105
Zumbrun, Kevin
9
2010
Nonlinear stability of semidiscrete shocks for two-sided schemes. Zbl 1219.35138
Beck, Margaret; Hupkes, Hermen Jan; Sandstede, Björn; Zumbrun, Kevin
7
2010
Long-time stability of multi-dimensional noncharacteristic viscous boundary layers. Zbl 1402.35228
Nguyen, Toan; Zumbrun, Kevin
5
2010
Stability of noncharacteristic boundary layers in the standing-shock limit. Zbl 1218.35180
Zumbrun, Kevin
4
2010
The refined inviscid stability condition and cellular instability of viscous shock waves. Zbl 1189.37081
Zumbrun, Kevin
4
2010
Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD. Zbl 1228.35049
Zumbrun, Kevin
3
2010
Spectral stability of ideal-gas shock layers. Zbl 1422.76122
Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
30
2009
Spectral stability of noncharacteristic isentropic Navier-Stokes boundary layers. Zbl 1169.76051
Costanzino, Nicola; Humpherys, Jeffrey; Nguyen, Toan; Zumbrun, Kevin
14
2009
Stability of undercompressive viscous shock profiles of hyperbolic-parabolic systems. Zbl 1170.35019
Raoofi, Mohammadreza; Zumbrun, Kevin
13
2009
Stability of scalar radiative shock profiles. Zbl 1218.35031
Lattanzio, Corrado; Mascia, Corrado; Nguyen, Toan; Plaza, Ramón G.; Zumbrun, Kevin
8
2009
Long-time stability of large-amplitude noncharacteristic boundary layers for hyperbolic-parabolic systems. Zbl 1188.35021
Nguyen, Toan; Zumbrun, Kevin
8
2009
Pointwise Green function bounds and long-time stability of large-amplitude noncharacteristic boundary layers. Zbl 1180.35145
Yarahmadian, Shantia; Zumbrun, Kevin
7
2009
Spectral stability of weak relaxation shock profiles. Zbl 1171.35076
Mascia, Corrado; Zumbrun, Kevin
7
2009
Conditional stability of unstable viscous shocks. Zbl 1175.35015
Zumbrun, Kevin
7
2009
Asymptotic behavior of multidimensional scalar relaxation shocks. Zbl 1188.35115
Kwon, Bongsuk; Zumbrun, Kevin
6
2009
Existence and sharp localization in velocity of small-amplitude Boltzmann shocks. Zbl 1197.76116
Métivier, Guy; Zumbrun, K.
5
2009
Existence of semilinear relaxation shocks. Zbl 1180.35358
Métivier, Guy; Zumbrun, Kevin
4
2009
Stability of viscous shocks in isentropic gas dynamics. Zbl 1171.35071
Barker, Blake; Humpherys, Jeffrey; Rudd, Keith; Zumbrun, Kevin
31
2008
Galloping instability of viscous shock waves. Zbl 1143.76439
Texier, Benjamin; Zumbrun, Kevin
25
2008
Hopf bifurcation of viscous shock waves in compressible gas dynamics and MHD. Zbl 1155.76037
Texier, Benjamin; Zumbrun, Kevin
23
2008
Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves. Zbl 1161.47058
Gesztesy, Fritz; Latushkin, Yuri; Zumbrun, Kevin
15
2008
Viscous boundary value problems for symmetric systems with variable multiplicities. Zbl 1138.35052
Gues, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
9
2008
Stability of isentropic Navier-Stokes shocks. Zbl 1152.76354
Barker, Blake; Humpherys, Jeffrey; Lafitte, Olivier; Rudd, Keith; Zumbrun, Kevin
7
2008
A sharp stability criterion for soliton-type propagating phase boundaries in Korteweg’s model. Zbl 1187.35229
Zumbrun, Kevin
5
2008
Nonclassical multidimensional viscous and inviscid shocks. Zbl 1162.35050
Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
3
2008
Transition to instability of planar viscous shock fronts: The refined stability condition. Zbl 1172.35060
Benzoni-Gavage, Sylvie; Serre, Denis; Zumbrun, Kevin
3
2008
Planar stability criteria for viscous shock waves of systems with real viscosity. Zbl 1138.35061
Zumbrun, Kevin
28
2007
Pointwise Green function bounds and stability of combustion waves. Zbl 1116.80017
Lyng, Gregory; Raoofi, Mohammadreza; Texier, Benjamin; Zumbrun, Kevin
16
2007
Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems. Zbl 1133.35404
Guès, Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
6
2007
Spectral stability conditions for shock wave patterns. Zbl 1147.35056
Lewicka, Marta; Zumbrun, Kevin
1
2007
An efficient shooting algorithm for Evans function calculations in large systems. Zbl 1101.65082
Humpherys, Jeffrey; Zumbrun, Kevin
51
2006
Stability of undercompressive shock profiles. Zbl 1102.35069
Howard, Peter; Zumbrun, Kevin
27
2006
Efficient computation of analytic bases in Evans function analysis of large systems. Zbl 1104.65081
Humpherys, Jeffrey; Sandstede, Björn; Zumbrun, Kevin
26
2006
Navier-Stokes regularization of multidimensional Euler shocks. Zbl 1173.35082
Guès, C. M. I. Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin
24
2006
Low-frequency stability analysis of periodic traveling-wave solutions of viscous conservation laws in several dimensions. Zbl 1099.35014
Oh, Myunghyun; Zumbrun, Kevin
11
2006
Sharp pointwise bounds for perturbed viscous shock waves. Zbl 1103.35073
Howard, Peter; Raoofi, Mohammadreza; Zumbrun, Kevin
10
2006
Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Zbl 1074.35066
Métivier, Guy; Zumbrun, Kevin
40
2005
...and 57 more Documents
all top 5

Cited by 836 Authors

98 Zumbrun, Kevin R.
21 Howard, Peter
20 Johnson, Mathew A.
19 Barker, Blake
18 Humpherys, Jeffrey
18 Wang, Weike
16 Métivier, Guy
16 Valdinoci, Enrico
15 Rodrigues, Luis Miguel
13 Lyng, Gregory Daniel
13 Williams, Mark
12 Nguyen, Toan Trong
12 Sandstede, Björn
11 Freistühler, Heinrich
11 Latushkin, Yuri
11 Marchesin, Dan
11 Xu, Jiang
10 Noble, Pascal
10 Wang, Jing
10 Wang, Wenjun
9 Hupkes, Hermen Jan
9 Jung, Soyeun
9 Plaza, Ramón G.
9 Ruan, Lizhi
9 Scheel, Arnd
9 Trakhinin, Yuri L.
9 Yang, Tong
8 Beck, Margaret
8 Duan, Renjun
8 Farina, Alberto
8 Guès, Olivier
8 Kagei, Yoshiyuki
8 Pogan, Alin
8 Rousset, Frédéric
8 Wu, Zhigang
8 Xie, Feng
8 Yao, Lei
8 Zhao, Huijiang
8 Zhu, Changjiang
7 Abreu, Eduardo
7 Fazly, Mostafa
7 Jones, Christopher K. R. T.
7 Lafitte, Olivier D.
7 Ma, Shixiang
7 Pinamonti, Andrea
7 Serre, Denis
7 Sukhtayev, Alim
7 Texier, Benjamin
7 Wang, Yuzhu
7 Yong, Wen-An
6 Bridges, Thomas J.
6 de Rijk, Björn
6 Ghazaryan, Anna
6 Guo, Boling
6 Haragus, Mariana
6 Kang, Moon-Jin
6 LeFloch, Philippe Gerard
6 Li, Tong
6 Liu, Hailiang
6 Marangell, Robert
6 Sire, Yannick
6 Ukai, Seiji
6 Vasseur, Alexis F.
6 Wei, Juncheng
6 Yao, Jinghua
5 Almog, Yaniv
5 Benzoni-Gavage, Sylvie
5 Chen, Gui-Qiang G.
5 Deconinck, Bernard
5 Huang, Feimin
5 Kawashima, Shuichi
5 Kwon, Bongsuk
5 Lafortune, Stéphane
5 Li, Hailiang
5 Milman, Emanuel
5 Ritoré, Manuel
5 Tan, Zhong
5 Wang, Yi
5 Wang, Zhian
5 Xi, Xiaoyu
5 Yao, Zhengan
5 Zhang, Ting
4 Beyn, Wolf-Jürgen
4 Bronski, Jared C.
4 Colombini, Ferruccio
4 Danchin, Raphaël
4 Del Santo, Daniele
4 Dipierro, Serena
4 Fan, Lili
4 Fanelli, Francesco
4 Ferrari, Fausto
4 Furtado, Frederico
4 Hamster, C. H. S.
4 Holzer, Matt
4 Ikehata, Ryo
4 Lee, Yongki
4 Lin, Xiaobiao
4 Liu, Tai-Ping
4 Mailybaev, Alexei A.
4 Matsumura, Akitaka
...and 736 more Authors
all top 5

Cited in 164 Serials

136 Journal of Differential Equations
68 Archive for Rational Mechanics and Analysis
44 Physica D
39 Journal of Mathematical Analysis and Applications
29 SIAM Journal on Mathematical Analysis
21 Journal of Hyperbolic Differential Equations
20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
19 Discrete and Continuous Dynamical Systems
18 Communications in Partial Differential Equations
16 Communications in Mathematical Physics
16 Transactions of the American Mathematical Society
15 ZAMP. Zeitschrift für angewandte Mathematik und Physik
15 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
13 Journal of Mathematical Physics
12 Quarterly of Applied Mathematics
12 Journal of Dynamics and Differential Equations
10 Journal de Mathématiques Pures et Appliquées. Neuvième Série
9 Journal of Functional Analysis
9 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
9 Journal of Nonlinear Science
9 Calculus of Variations and Partial Differential Equations
9 NoDEA. Nonlinear Differential Equations and Applications
9 Communications on Pure and Applied Analysis
8 Communications on Pure and Applied Mathematics
8 Mathematical Methods in the Applied Sciences
8 Nonlinear Analysis. Real World Applications
8 SIAM Journal on Applied Dynamical Systems
7 Zeitschrift für Analysis und ihre Anwendungen
7 The Journal of Geometric Analysis
7 Kinetic and Related Models
6 Proceedings of the American Mathematical Society
6 Studies in Applied Mathematics
5 Applicable Analysis
5 Journal of Fluid Mechanics
5 Chinese Annals of Mathematics. Series B
5 Applied Mathematics Letters
5 SIAM Journal on Applied Mathematics
5 Journal of Mathematical Fluid Mechanics
5 Discrete and Continuous Dynamical Systems. Series B
4 Advances in Mathematics
4 Annales de l’Institut Fourier
4 Indiana University Mathematics Journal
4 Mathematische Annalen
4 Science China. Mathematics
4 Advances in Nonlinear Analysis
3 Computers & Mathematics with Applications
3 Nonlinearity
3 Duke Mathematical Journal
3 Publications of the Research Institute for Mathematical Sciences, Kyoto University
3 Acta Applicandae Mathematicae
3 Acta Mathematicae Applicatae Sinica. English Series
3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Acta Mathematica Sinica. English Series
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Bulletin of the Brazilian Mathematical Society. New Series
3 Discrete and Continuous Dynamical Systems. Series S
3 Analysis and Geometry in Metric Spaces
3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
2 Journal d’Analyse Mathématique
2 Journal of Computational Physics
2 Journal of Mathematical Biology
2 Mathematics of Computation
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
2 Applied Mathematics and Computation
2 Archiv der Mathematik
2 Integral Equations and Operator Theory
2 Inventiones Mathematicae
2 Journal of Computational and Applied Mathematics
2 Journal für die Reine und Angewandte Mathematik
2 Numerische Mathematik
2 Osaka Journal of Mathematics
2 SIAM Journal on Numerical Analysis
2 Journal of the American Mathematical Society
2 Journal of Scientific Computing
2 Wuhan University Journal of Natural Sciences (WUJNS)
2 Journal of the European Mathematical Society (JEMS)
2 Computational Geosciences
2 Combustion Theory and Modelling
2 Communications in Contemporary Mathematics
2 Journal of Evolution Equations
2 Acta Mathematica Scientia. Series B. (English Edition)
2 Multiscale Modeling & Simulation
2 Journal of the Institute of Mathematics of Jussieu
2 Analysis and Applications (Singapore)
2 Frontiers of Mathematics in China
2 Networks and Heterogeneous Media
2 Journal de l’École Polytechnique – Mathématiques
1 Computers and Fluids
1 Israel Journal of Mathematics
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Journal of Engineering Mathematics
1 Journal of the Mechanics and Physics of Solids
1 Journal of Statistical Physics
1 Mathematical Biosciences
1 Physics Letters. A
1 Russian Mathematical Surveys
1 Theoretical and Mathematical Physics
1 Transport Theory and Statistical Physics
...and 64 more Serials
all top 5

Cited in 40 Fields

729 Partial differential equations (35-XX)
341 Fluid mechanics (76-XX)
58 Ordinary differential equations (34-XX)
52 Dynamical systems and ergodic theory (37-XX)
45 Numerical analysis (65-XX)
31 Calculus of variations and optimal control; optimization (49-XX)
30 Differential geometry (53-XX)
29 Operator theory (47-XX)
27 Statistical mechanics, structure of matter (82-XX)
26 Mechanics of deformable solids (74-XX)
25 Classical thermodynamics, heat transfer (80-XX)
21 Biology and other natural sciences (92-XX)
20 Optics, electromagnetic theory (78-XX)
19 Global analysis, analysis on manifolds (58-XX)
12 Harmonic analysis on Euclidean spaces (42-XX)
9 Quantum theory (81-XX)
8 Convex and discrete geometry (52-XX)
8 Probability theory and stochastic processes (60-XX)
7 Operations research, mathematical programming (90-XX)
6 Systems theory; control (93-XX)
5 Functional analysis (46-XX)
5 Geophysics (86-XX)
4 Real functions (26-XX)
4 Potential theory (31-XX)
3 Measure and integration (28-XX)
3 Functions of a complex variable (30-XX)
3 Difference and functional equations (39-XX)
3 Statistics (62-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Integral equations (45-XX)
2 Computer science (68-XX)
2 Mechanics of particles and systems (70-XX)
2 Astronomy and astrophysics (85-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Algebraic geometry (14-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Integral transforms, operational calculus (44-XX)
1 Manifolds and cell complexes (57-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year