## Martel, Yvan

Compute Distance To:
 Author ID: martel.yvan Published as: Martel, Yvan; Martel, Y. External Links: MGP · Wikidata · IdRef · theses.fr
 Documents Indexed: 85 Publications since 1995 Reviewing Activity: 16 Reviews Co-Authors: 31 Co-Authors with 72 Joint Publications 649 Co-Co-Authors
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### Co-Authors

 13 single-authored 35 Merle, Frank 11 Raphael, Pierre 6 Cazenave, Thierry 5 Côte, Raphaël 5 Kowalczyk, Michał 5 Muñoz, Claudio 4 Kenig, Carlos Eduardo 4 Zhao, Lifeng 2 Brézis, Haïm 2 Cabré, Xavier 2 Combet, Vianney 2 Laurent, Celine 2 Pilod, Didier 2 Ramiandrisoa, Arthur 2 Souplet, Philippe 2 Tsai, Tai-Peng 2 Yuan, Xu 1 Bahri, Yakine 1 de Bouard, Anne 1 Duyckaerts, Thomas 1 El Dika, Khaled 1 Han, Zheng 1 Jendrej, Jacek 1 Krieger, Joachim 1 Le Coz, Stefan 1 Mizumachi, Tetsu 1 Nakanishi, Kenji 1 Nguyen, Tien Vinh 1 Robbiano, Luc 1 Szeftel, Jérémie 1 Van Den Bosch, Hanne
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### Serials

 6 Communications in Mathematical Physics 5 Archive for Rational Mechanics and Analysis 4 Discrete and Continuous Dynamical Systems 3 Mathematische Annalen 3 Transactions of the American Mathematical Society 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Revista Matemática Iberoamericana 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Duke Mathematical Journal 2 Inventiones Mathematicae 2 Journal of the American Mathematical Society 2 Communications in Partial Differential Equations 2 SIAM Journal on Mathematical Analysis 2 Séminaire Équations aux Dérivées Partielles 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Annals of Mathematics. Second Series 2 Journal of the European Mathematical Society (JEMS) 2 Séminaire Laurent Schwartz. EDP et Applications 1 Communications on Pure and Applied Mathematics 1 Houston Journal of Mathematics 1 Letters in Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Nonlinearity 1 Russian Mathematical Surveys 1 Acta Mathematica 1 American Journal of Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Gazette des Mathématiciens 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Portugaliae Mathematica 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Journal of Dynamics and Differential Equations 1 Advances in Mathematical Sciences and Applications 1 Computational and Applied Mathematics 1 Bulletin des Sciences Mathématiques 1 Advances in Differential Equations 1 Revista Matemática Complutense 1 Annales Henri Poincaré 1 Advanced Nonlinear Studies 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Dynamics of Partial Differential Equations 1 Boletín de la Sociedad Española de Matemática Aplicada. S$$\vec{\text{e}}$$MA 1 Nonlinear Analysis. Theory, Methods & Applications 1 Annals of PDE
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### Fields

 85 Partial differential equations (35-XX) 28 Dynamical systems and ergodic theory (37-XX) 3 Fluid mechanics (76-XX) 1 Ordinary differential equations (34-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

72 Publications have been cited 1,614 times in 698 Documents Cited by Year
Blow up for $$u_ t- \Delta u=g(u)$$ revisited. Zbl 0855.35063
Brézis, Haim; Cazenave, Thierry; Martel, Yvan; Ramiandrisoa, Arthur
1996
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2002
Existence versus instantaneous blow-up for linear heat equations with singular potentials. (Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier.) Zbl 0940.35105
Cabré, Xavier; Martel, Yvan
1999
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
2001
Asymptotic $$N$$-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations. Zbl 1090.35158
Martel, Yvan
2005
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
2000
Blow up in finite time and dynamics of blow up solutions for the $$L^2$$-critical generalized KdV equation. Zbl 0996.35064
Martel, Yvan; Merle, Frank
2002
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
2001
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
2005
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
2006
Stability in $$H^1$$ of the sum of $$K$$ solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2006
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081
Martel, Yvan; Merle, Frank
2002
Construction of multi-soliton solutions for the $$L^2$$-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
2011
Kink dynamics in the $$\phi^4$$ model: asymptotic stability for odd perturbations in the energy space. Zbl 1387.35419
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio
2017
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
2008
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2014
Weak eigenfunctions for the linearization of extremal elliptic problems. Zbl 0908.35044
Cabré, Xavier; Martel, Yvan
1998
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
2011
Local well-posedness and blow-up in the energy space for a class of $$L^2$$ critical dispersion generalized Benjamin-Ono equations. Zbl 1230.35102
Kenig, C. E.; Martel, Y.; Robbiano, L.
2011
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Asymptotic stability of solitons for the Benjamin-Ono equation. Zbl 1247.35133
Kenig, Carlos E.; Martel, Yvan
2009
Two-soliton solutions to the three-dimensional gravitational Hartree equation. Zbl 1193.35163
Krieger, Joachim; Raphaël, Pierre; Martel, Yvan
2009
Uniqueness of weak extremal solutions of nonlinear elliptic problems. Zbl 0884.35037
Martel, Yvan
1997
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
2011
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
2009
Nonexistence of small, odd breathers for a class of nonlinear wave equations. Zbl 1384.35109
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio
2017
Nonexistence of blow-up solution with minimal $$L^2$$-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
2002
Linear problems related to asymptotic stability of solitons of the generalized KdV equations. Zbl 1126.35055
Martel, Yvan
2006
Strongly interacting blow up bubbles for the mass critical nonlinear Schrödinger equation. Zbl 1403.35280
Martel, Yvan; Raphaël, Pierre
2018
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
2016
Complete blow up and global behaviour of solutions of $$u_t- \Delta u=g(u)$$. Zbl 0914.35057
Martel, Yvan
1998
Minimal mass blow up solutions for a double power nonlinear Schrödinger equation. Zbl 1354.35141
Le Coz, Stefan; Martel, Yvan; Raphaël, Pierre
2016
Stability of $$N$$ solitary waves for the generalized BBM equations. Zbl 1080.35116
El Dika, Khaled; Martel, Yvan
2004
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
2016
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
2008
Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation. Zbl 1391.35077
Martel, Yvan; Pilod, Didier
2017
Multi-travelling waves for the nonlinear Klein-Gordon equation. Zbl 1403.35260
Côte, Raphaël; Martel, Yvan
2018
Non existence of $$L^2$$-compact solutions of the Kadomtsev-Petviashvili II equation. Zbl 1330.35389
de Bouard, Anne; Martel, Yvan
2004
Blow-up for the nonlinear Schrödinger equation in nonisotropic spaces. Zbl 0872.35102
Martel, Yvan
1997
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
2010
Finite-time blowup for a Schrödinger equation with nonlinear source term. Zbl 1404.35405
Cazenave, Thierry; Martel, Yvan; Zhao, Lifeng
2019
Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079
Martel, Yvan; Souplet, Philippe
2000
Global well-posedness in the energy space for a modified KP II equation via the Miura transform. Zbl 1106.35082
Kenig, Carlos E.; Martel, Yvan
2006
Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg-de Vries equation. Zbl 1219.35248
Martel, Yvan; Merle, Frank
2011
Smoothness and exponential decay of $$L^2$$-compact solutions of the generalized KdV equations. Zbl 1140.35558
Laurent, Celine; Martel, Yvan
2004
Construction of multibubble solutions for the critical gKdV equation. Zbl 1397.35249
Combet, Vianney; Martel, Yvan
2018
Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165
Martel, Yvan; Merle, Frank
2010
A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models. Zbl 1469.35150
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio; Van Den Bosch, Hanne
2021
Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. Zbl 1188.35164
Martel, Yvan; Merle, Frank
2008
Blow up and near soliton dynamics for the $$L^2$$ critical gKdV equation. Zbl 1319.35224
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2013
Near soliton dynamics and singularity formation for $$L^2$$ critical problems. Zbl 1304.35650
Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J.
2014
On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191
Martel, Yvan; Merle, Frank
2015
Solutions blowing up on any given compact set for the energy subcritical wave equation. Zbl 1437.35493
Cazenave, Thierry; Martel, Yvan; Zhao, Lifeng
2020
Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation. Zbl 1464.35028
Côte, Raphaël; Martel, Yvan; Yuan, Xu
2021
Smoothness and exponential decay of $$L^2$$-compact solutions of the generalized KdV equations. Zbl 1060.35125
Laurent, Celine; Martel, Yvan
2003
Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation. Zbl 1423.35334
Combet, Vianney; Martel, Yvan
2017
Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111
Martel, Yvan; Merle, Frank
2018
Construction of 2-solitons with logarithmic distance for the one-dimensional cubic Schrödinger system. Zbl 1439.35442
Martel, Yvan; Nguyến, Tiễn Vinh
2020
Solutions with prescribed local blow-up surface for the nonlinear wave equation. Zbl 1437.35494
Cazenave, Thierry; Martel, Yvan; Zhao, Lifeng
2019
Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114
Martel, Yvan; Merle, Frank
2004
Small time boundary estimates for solutions of the heat equation with non-compatible data. (Estimation optimales en temps petit et près de la frontière pour les solutions de l’équation de la chaleur avec données non compatibles.) Zbl 0990.35051
Martel, Yvan; Souplet, Philippe
1998
Dynamical instability of singular extremal solutions of nonlinear elliptic problems. Zbl 0932.35070
Martel, Yvan
1999
Description and classification of $$2$$-solitary waves for nonlinear damped Klein-Gordon equations. Zbl 1477.35210
Côte, Raphaël; Martel, Yvan; Yuan, Xu; Zhao, Lifeng
2021
Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5. Zbl 1471.35205
Jendrej, Jacek; Martel, Yvan
2020
Soliton resolution for critical co-rotational wave maps and radial cubic wave equation. Zbl 1491.35292
Duyckaerts, Thomas; Kenig, Carlos; Martel, Yvan; Merle, Frank
2022
Blowup on an arbitrary compact set for a Schrödinger equation with nonlinear source term. Zbl 1466.35323
Cazenave, Thierry; Han, Zheng; Martel, Yvan
2021
Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes. Zbl 1486.35122
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio
2022
A wave equation with a Dirac distribution. Zbl 0849.35019
Martel, Yvan
1995
Qualitative results on the generalized critical KdV equation. Zbl 1044.35074
Martel, Yvan; Merle, Frank
2003
Multi-solitons and large time dynamics of some nonlinear dispersive equations. Zbl 1244.35118
Martel, Yvan
2005
Interaction of solitons from the PDE point of view. Zbl 1447.35007
Martel, Yvan
2018
Soliton resolution for critical co-rotational wave maps and radial cubic wave equation. Zbl 1491.35292
Duyckaerts, Thomas; Kenig, Carlos; Martel, Yvan; Merle, Frank
2022
Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes. Zbl 1486.35122
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio
2022
A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models. Zbl 1469.35150
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio; Van Den Bosch, Hanne
2021
Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation. Zbl 1464.35028
Côte, Raphaël; Martel, Yvan; Yuan, Xu
2021
Description and classification of $$2$$-solitary waves for nonlinear damped Klein-Gordon equations. Zbl 1477.35210
Côte, Raphaël; Martel, Yvan; Yuan, Xu; Zhao, Lifeng
2021
Blowup on an arbitrary compact set for a Schrödinger equation with nonlinear source term. Zbl 1466.35323
Cazenave, Thierry; Han, Zheng; Martel, Yvan
2021
Solutions blowing up on any given compact set for the energy subcritical wave equation. Zbl 1437.35493
Cazenave, Thierry; Martel, Yvan; Zhao, Lifeng
2020
Construction of 2-solitons with logarithmic distance for the one-dimensional cubic Schrödinger system. Zbl 1439.35442
Martel, Yvan; Nguyến, Tiễn Vinh
2020
Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5. Zbl 1471.35205
Jendrej, Jacek; Martel, Yvan
2020
Finite-time blowup for a Schrödinger equation with nonlinear source term. Zbl 1404.35405
Cazenave, Thierry; Martel, Yvan; Zhao, Lifeng
2019
Solutions with prescribed local blow-up surface for the nonlinear wave equation. Zbl 1437.35494
Cazenave, Thierry; Martel, Yvan; Zhao, Lifeng
2019
Strongly interacting blow up bubbles for the mass critical nonlinear Schrödinger equation. Zbl 1403.35280
Martel, Yvan; Raphaël, Pierre
2018
Multi-travelling waves for the nonlinear Klein-Gordon equation. Zbl 1403.35260
Côte, Raphaël; Martel, Yvan
2018
Construction of multibubble solutions for the critical gKdV equation. Zbl 1397.35249
Combet, Vianney; Martel, Yvan
2018
Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111
Martel, Yvan; Merle, Frank
2018
Interaction of solitons from the PDE point of view. Zbl 1447.35007
Martel, Yvan
2018
Kink dynamics in the $$\phi^4$$ model: asymptotic stability for odd perturbations in the energy space. Zbl 1387.35419
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio
2017
Nonexistence of small, odd breathers for a class of nonlinear wave equations. Zbl 1384.35109
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio
2017
Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation. Zbl 1391.35077
Martel, Yvan; Pilod, Didier
2017
Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation. Zbl 1423.35334
Combet, Vianney; Martel, Yvan
2017
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
2016
Minimal mass blow up solutions for a double power nonlinear Schrödinger equation. Zbl 1354.35141
Le Coz, Stefan; Martel, Yvan; Raphaël, Pierre
2016
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
2016
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191
Martel, Yvan; Merle, Frank
2015
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2014
Near soliton dynamics and singularity formation for $$L^2$$ critical problems. Zbl 1304.35650
Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J.
2014
Blow up and near soliton dynamics for the $$L^2$$ critical gKdV equation. Zbl 1319.35224
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2013
Construction of multi-soliton solutions for the $$L^2$$-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
2011
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
2011
Local well-posedness and blow-up in the energy space for a class of $$L^2$$ critical dispersion generalized Benjamin-Ono equations. Zbl 1230.35102
Kenig, C. E.; Martel, Y.; Robbiano, L.
2011
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
2011
Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg-de Vries equation. Zbl 1219.35248
Martel, Yvan; Merle, Frank
2011
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
2010
Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165
Martel, Yvan; Merle, Frank
2010
Asymptotic stability of solitons for the Benjamin-Ono equation. Zbl 1247.35133
Kenig, Carlos E.; Martel, Yvan
2009
Two-soliton solutions to the three-dimensional gravitational Hartree equation. Zbl 1193.35163
Krieger, Joachim; Raphaël, Pierre; Martel, Yvan
2009
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
2009
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
2008
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
2008
Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. Zbl 1188.35164
Martel, Yvan; Merle, Frank
2008
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
2006
Stability in $$H^1$$ of the sum of $$K$$ solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2006
Linear problems related to asymptotic stability of solitons of the generalized KdV equations. Zbl 1126.35055
Martel, Yvan
2006
Global well-posedness in the energy space for a modified KP II equation via the Miura transform. Zbl 1106.35082
Kenig, Carlos E.; Martel, Yvan
2006
Asymptotic $$N$$-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations. Zbl 1090.35158
Martel, Yvan
2005
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
2005
Multi-solitons and large time dynamics of some nonlinear dispersive equations. Zbl 1244.35118
Martel, Yvan
2005
Stability of $$N$$ solitary waves for the generalized BBM equations. Zbl 1080.35116
El Dika, Khaled; Martel, Yvan
2004
Non existence of $$L^2$$-compact solutions of the Kadomtsev-Petviashvili II equation. Zbl 1330.35389
de Bouard, Anne; Martel, Yvan
2004
Smoothness and exponential decay of $$L^2$$-compact solutions of the generalized KdV equations. Zbl 1140.35558
Laurent, Celine; Martel, Yvan
2004
Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114
Martel, Yvan; Merle, Frank
2004
Smoothness and exponential decay of $$L^2$$-compact solutions of the generalized KdV equations. Zbl 1060.35125
Laurent, Celine; Martel, Yvan
2003
Qualitative results on the generalized critical KdV equation. Zbl 1044.35074
Martel, Yvan; Merle, Frank
2003
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2002
Blow up in finite time and dynamics of blow up solutions for the $$L^2$$-critical generalized KdV equation. Zbl 0996.35064
Martel, Yvan; Merle, Frank
2002
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081
Martel, Yvan; Merle, Frank
2002
Nonexistence of blow-up solution with minimal $$L^2$$-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
2002
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
2001
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
2001
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
2000
Small time boundary behavior of solutions of parabolic equations with noncompatible data. Zbl 0959.35079
Martel, Yvan; Souplet, Philippe
2000
Existence versus instantaneous blow-up for linear heat equations with singular potentials. (Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier.) Zbl 0940.35105
Cabré, Xavier; Martel, Yvan
1999
Dynamical instability of singular extremal solutions of nonlinear elliptic problems. Zbl 0932.35070
Martel, Yvan
1999
Weak eigenfunctions for the linearization of extremal elliptic problems. Zbl 0908.35044
Cabré, Xavier; Martel, Yvan
1998
Complete blow up and global behaviour of solutions of $$u_t- \Delta u=g(u)$$. Zbl 0914.35057
Martel, Yvan
1998
Small time boundary estimates for solutions of the heat equation with non-compatible data. (Estimation optimales en temps petit et près de la frontière pour les solutions de l’équation de la chaleur avec données non compatibles.) Zbl 0990.35051
Martel, Yvan; Souplet, Philippe
1998
Uniqueness of weak extremal solutions of nonlinear elliptic problems. Zbl 0884.35037
Martel, Yvan
1997
Blow-up for the nonlinear Schrödinger equation in nonisotropic spaces. Zbl 0872.35102
Martel, Yvan
1997
Blow up for $$u_ t- \Delta u=g(u)$$ revisited. Zbl 0855.35063
Brézis, Haim; Cazenave, Thierry; Martel, Yvan; Ramiandrisoa, Arthur
1996
A wave equation with a Dirac distribution. Zbl 0849.35019
Martel, Yvan
1995
all top 5

### Cited by 715 Authors

 47 Martel, Yvan 33 Merle, Frank 30 Muñoz, Claudio 28 Raphael, Pierre 14 Côte, Raphaël 11 Kenig, Carlos Eduardo 10 Diaz Diaz, Jesus Ildefonso 9 Cuccagna, Scipio 9 Jendrej, Jacek 9 Ponce, Gustavo 8 Duyckaerts, Thomas 8 Holmer, Justin 8 Klein, Christian 8 Kombe, Ismail 8 Liu, Yue 8 Mizumachi, Tetsu 8 Molinet, Luc 8 Saut, Jean-Claude 8 Vazquez, Juan Luis 8 Zaag, Hatem 7 Cazenave, Thierry 7 Filippas, Stathis 7 Goldstein, Jerome Arthur 7 Roudenko, Svetlana 7 Tertikas, Achilles 7 Wang, Zhong 7 Yuan, Xu 6 Alejo, Miguel A. 6 Cowan, Craig 6 Farah, Luiz Gustavo 6 Kowalczyk, Michał 6 Linares, Felipe 6 Maeda, Masaya 6 Palacios, José Manuel 6 Rakotoson, Jean-Michel 6 Souplet, Philippe 5 Abdellaoui, Boumediene 5 Angulo Pava, Jaime 5 Dávila, Juan 5 Krieger, Joachim 5 Le Coz, Stefan 5 Lenzmann, Enno 5 Pigott, Brian 5 Qu, Changzheng 5 Szeftel, Jérémie 5 Zographopoulos, Nikolaos B. 5 Zuazua, Enrique 4 Canale, Anna 4 Chen, Gong 4 Collot, Charles 4 Combet, Vianney 4 Ferrero, Alberto 4 Gazzola, Filippo 4 Ghoul, Tej-Eddine 4 Ghoussoub, Nassif A. 4 Gravejat, Philippe 4 Koch, Herbert 4 Komech, Alexander Ilich 4 Korpusov, Maksim Olegovich 4 Lai, Baishun 4 Liu, Xiaochuan 4 Liu, Xingxing 4 Peral Alonso, Ireneo 4 Pilod, Didier 4 Primo, Ana R. M. 4 Rhandi, Abdelaziz 4 Rossi, Julio Daniel 4 Soffer, Avraham 4 Takahashi, Futoshi 4 Tao, Terence 4 Tsai, Tai-Peng 4 Wang, Qi 4 Wei, Juncheng 4 Zhao, Lifeng 3 Barbatis, Gerassimos 3 Ben Mabrouk, Anouar 3 Berchio, Elvise 3 Bona, Jerry Lloyd 3 Cabré, Xavier 3 Carles, Rémi 3 Carvajal, Xavier Paredes 3 Chan, Hardy 3 Chen, Jiajie 3 Cui, Shangbin 3 de Laire, André 3 Dinh, Van Duong 3 Dupaigne, Louis 3 El Dika, Khaled 3 Fazly, Mostafa 3 Ferreira, Lucas Catão de Freitas 3 Fiorenza, Alberto 3 Fonseca, Germán Eduardo 3 Forcella, Luigi 3 Georgiev, Vladimir S. 3 Germain, Pierre 3 Grunau, Hans-Christoph 3 Guo, Zihua 3 Han, Zheng 3 Kabakouala, André 3 Kazeykina, Anna ...and 615 more Authors
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### Cited in 143 Serials

 50 Journal of Differential Equations 33 Journal of Mathematical Analysis and Applications 29 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 28 Communications in Mathematical Physics 27 Journal of Functional Analysis 27 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 23 Archive for Rational Mechanics and Analysis 23 Discrete and Continuous Dynamical Systems 17 Nonlinearity 17 Transactions of the American Mathematical Society 17 Communications in Partial Differential Equations 16 Proceedings of the American Mathematical Society 14 Calculus of Variations and Partial Differential Equations 14 Communications on Pure and Applied Analysis 14 Séminaire Laurent Schwartz. EDP et Applications 12 SIAM Journal on Mathematical Analysis 10 Physica D 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Journal of Evolution Equations 8 Applicable Analysis 8 Advanced Nonlinear Studies 7 Journal of Mathematical Physics 7 Journal of the American Mathematical Society 7 Journal of Nonlinear Science 7 Communications in Contemporary Mathematics 6 Journal d’Analyse Mathématique 6 Inventiones Mathematicae 6 Mathematische Annalen 6 Journal of Dynamics and Differential Equations 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Communications on Pure and Applied Mathematics 5 Duke Mathematical Journal 5 Memoirs of the American Mathematical Society 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 NoDEA. Nonlinear Differential Equations and Applications 5 Nonlinear Analysis. Real World Applications 5 Journal of Hyperbolic Differential Equations 5 Annals of PDE 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Applied Mathematics and Computation 4 Revista Matemática Iberoamericana 4 Journal of the European Mathematical Society (JEMS) 4 Annales Henri Poincaré 4 Discrete and Continuous Dynamical Systems. Series B 4 Analysis & PDE 4 Differential Equations and Applications 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 4 SN Partial Differential Equations and Applications 3 Letters in Mathematical Physics 3 Mathematical Methods in the Applied Sciences 3 Advances in Mathematics 3 Annales de l’Institut Fourier 3 Quarterly of Applied Mathematics 3 Chinese Annals of Mathematics. Series B 3 Applied Mathematics Letters 3 Geometric and Functional Analysis. GAFA 3 Izvestiya: Mathematics 3 Discrete and Continuous Dynamical Systems. Series S 3 Science China. Mathematics 2 Rocky Mountain Journal of Mathematics 2 Wave Motion 2 Acta Mathematica 2 Applied Mathematics and Optimization 2 Archiv der Mathematik 2 Journal of Computational and Applied Mathematics 2 Mathematische Nachrichten 2 Zeitschrift für Analysis und ihre Anwendungen 2 The Journal of Geometric Analysis 2 Potential Analysis 2 Journal of Mathematical Fluid Mechanics 2 Annals of Mathematics. Second Series 2 Acta Mathematica Sinica. English Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Journal of High Energy Physics 2 Stochastics and Dynamics 2 S$$\vec{\text{e}}$$MA Journal 2 Advances in Nonlinear Analysis 2 Journal of Elliptic and Parabolic Equations 2 Journal of Ramanujan Society of Mathematics and Mathematical Sciences 2 Electronic Research Archive 1 Journal of Computational Physics 1 Journal of Statistical Physics 1 Nuclear Physics. B 1 Physics Letters. A 1 Russian Mathematical Surveys 1 Theoretical and Mathematical Physics 1 Mathematics of Computation 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Publications Mathématiques 1 Journal of the London Mathematical Society. Second Series 1 Manuscripta Mathematica 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the London Mathematical Society. Third Series 1 Ricerche di Matematica 1 Studies in Applied Mathematics ...and 43 more Serials
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### Cited in 32 Fields

 675 Partial differential equations (35-XX) 103 Dynamical systems and ergodic theory (37-XX) 48 Fluid mechanics (76-XX) 35 Real functions (26-XX) 27 Functional analysis (46-XX) 23 Operator theory (47-XX) 23 Quantum theory (81-XX) 22 Numerical analysis (65-XX) 18 Ordinary differential equations (34-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 10 Mechanics of deformable solids (74-XX) 10 Systems theory; control (93-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 7 Differential geometry (53-XX) 7 Global analysis, analysis on manifolds (58-XX) 5 Probability theory and stochastic processes (60-XX) 5 Optics, electromagnetic theory (78-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Relativity and gravitational theory (83-XX) 4 Biology and other natural sciences (92-XX) 3 Potential theory (31-XX) 3 Difference and functional equations (39-XX) 3 Integral equations (45-XX) 3 Statistics (62-XX) 3 Mechanics of particles and systems (70-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Astronomy and astrophysics (85-XX) 2 Topological groups, Lie groups (22-XX) 2 Special functions (33-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX)

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