×
Author ID: debussche.arnaud Recent zbMATH articles by "Debussche, Arnaud"
Published as: Debussche, Arnaud; Debussche, A.
all top 5

Serials

7 Journal of Functional Analysis
5 Journal de Mathématiques Pures et Appliquées. Neuvième Série
5 Stochastic and Partial Differential Equations. Analysis and Computations
4 The Annals of Probability
4 Applied Mathematics and Optimization
4 Physica D
4 Probability Theory and Related Fields
4 Applied Mathematics Letters
4 SIAM Journal on Mathematical Analysis
3 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
3 Differential and Integral Equations
3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
3 Electronic Communications in Probability
3 Journal of Evolution Equations
2 Nonlinearity
2 Mathematics of Computation
2 Numerische Mathematik
2 SIAM Journal on Numerical Analysis
2 Stochastic Analysis and Applications
2 Asymptotic Analysis
2 The Annals of Applied Probability
2 Stochastic Processes and their Applications
2 Journal of Dynamics and Differential Equations
2 Séminaire Équations aux Dérivées Partielles
2 Electronic Journal of Probability
2 Discrete and Continuous Dynamical Systems
2 Lecture Notes in Mathematics
2 Nonlinear Analysis. Theory, Methods & Applications
1 Communications in Mathematical Physics
1 International Journal for Numerical Methods in Fluids
1 Journal of Computational Physics
1 Journal of Statistical Physics
1 Theoretical and Computational Fluid Dynamics
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Journal of Differential Equations
1 Numerical Functional Analysis and Optimization
1 SIAM Journal on Control and Optimization
1 Theoretical Computer Science
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Numerical Methods for Partial Differential Equations
1 Journal of Scientific Computing
1 IMRN. International Mathematics Research Notices
1 Stochastics and Stochastics Reports
1 Potential Analysis
1 NoDEA. Nonlinear Differential Equations and Applications
1 Monte Carlo Methods and Applications
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Infinite Dimensional Analysis, Quantum Probability and Related Topics
1 Journal of Mathematical Fluid Mechanics
1 Journal of Computational Analysis and Applications
1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
1 Discrete and Continuous Dynamical Systems. Series B
1 Communications on Pure and Applied Analysis
1 Discrete and Continuous Dynamical Systems. Series S
1 Kinetic and Related Models
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys
1 Tunisian Journal of Mathematics
1 Pure and Applied Analysis

Publications by Year

Citations contained in zbMATH Open

112 Publications have been cited 3,506 times in 2,212 Documents Cited by Year
Random attractors. Zbl 0884.58064
Crauel, Hans; Debussche, Arnaud; Flandoli, Franco
525
1997
Strong solutions to the stochastic quantization equations. Zbl 1071.81070
Da Prato, Giuseppe; Debussche, Arnaud
139
2003
Stochastic Burgers’ equation. Zbl 0824.35112
Da Prato, Giuseppe; Debussche, Arnaud; Temam, Roger
126
1994
Two-dimensional Navier-Stokes equations driven by a space-time white noise. Zbl 1013.60051
Da Prato, Giuseppe; Debussche, Arnaud
113
2002
The stochastic nonlinear Schrödinger equation in \(H^1\). Zbl 1027.60065
de Bouard, A.; Debussche, A.
108
2003
Stochastic Cahn-Hilliard equation. Zbl 0838.60056
Da Prato, Giuseppe; Debussche, Arnaud
105
1996
Scalar conservation laws with stochastic forcing. Zbl 1200.60050
Debussche, A.; Vovelle, J.
100
2010
Ergodicity for the 3D stochastic Navier-Stokes equations. Zbl 1109.60047
Da Prato, Giuseppe; Debussche, Arnaud
95
2003
A stochastic nonlinear Schrödinger equation with multiplicative noise. Zbl 0952.60061
de Bouard, A.; Debussche, A.
89
1999
Local martingale and pathwise solutions for an abstract fluids model. Zbl 1230.60065
Debussche, Arnaud; Glatt-Holtz, Nathan; Temam, Roger
89
2011
On the stochastic Korteweg-de Vries equation. Zbl 0912.60074
de Bouard, A.; Debussche, A.
79
1998
On the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0831.35088
Debussche, Arnaud; Dettori, Lucia
74
1995
White noise driven Korteweg-de Vries equation. Zbl 0952.60062
de Bouard, A.; Debussche, A.; Tsutsumi, Y.
68
1999
Numerical simulation of the stochastic Korteweg-de Vries equation. Zbl 0948.76038
Debussche, Arnaud; Printems, Jacques
63
1999
Degenerate parabolic stochastic partial differential equations: quasilinear case. Zbl 1346.60094
Debussche, Arnaud; Hofmanová, Martina; Vovelle, Julien
63
2016
Hausdorff dimension of a random invariant set. Zbl 0919.58044
Debussche, A.
61
1998
Convergence of stochastic gene networks to hybrid piecewise deterministic processes. Zbl 1261.60073
Crudu, A.; Debussche, A.; Muller, A.; Radulescu, O.
51
2012
Weak order for the discretization of the stochastic heat equation. Zbl 1215.60043
Debussche, Arnaud; Printems, Jacques
49
2009
Weak approximation of stochastic partial differential equations: the nonlinear case. Zbl 1217.65011
Debussche, Arnaud
49
2011
On the finite dimensionality of random attractors. Zbl 0888.60051
Debussche, A.
47
1997
Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise. Zbl 1068.35191
de Bouard, Anne; Debussche, Arnaud
46
2005
Numerical simulation of focusing stochastic nonlinear Schrödinger equations. Zbl 0988.35156
Debussche, Arnaud; Di Menza, Laurent
44
2002
Ergodicity results for the stochastic Navier-Stokes equations: an introduction. Zbl 1301.35086
Debussche, Arnaud
44
2013
Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise. Zbl 1246.35194
Debussche, A.; Glatt-Holtz, N.; Temam, R.; Ziane, M.
39
2012
On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation. Zbl 1008.35074
de Bouard, A.; Debussche, A.
38
2002
Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrödinger equation. Zbl 1109.60051
de Bouard, Anne; Debussche, Arnaud
38
2006
Markov solutions for the 3D stochastic Navier-Stokes equations with state dependent noise. Zbl 1110.35110
Debussche, Arnaud; Odasso, Cyril
35
2006
The nonlinear Schrödinger equation with white noise dispersion. Zbl 1193.35213
de Bouard, Anne; Debussche, Arnaud
34
2010
Invariant measure of scalar first-order conservation laws with stochastic forcing. Zbl 1331.60117
Debussche, A.; Vovelle, J.
34
2015
Effect of a localized random forcing term on the Korteweg-de Vries equation. Zbl 1032.35155
Debussche, Arnaud; Printems, Jacques
32
2001
A semi-discrete scheme for the stochastic nonlinear Schrödinger equation. Zbl 1055.65008
de Bouard, A.; Debussche, A.
32
2004
1D quintic nonlinear Schrödinger equation with white noise dispersion. Zbl 1234.35242
Debussche, Arnaud; Tsutsumi, Yoshio
32
2011
Conservative stochastic Cahn-Hilliard equation with reflection. Zbl 1130.60068
Debussche, Arnaud; Zambotti, Lorenzo
30
2007
Ergodicity for a weakly damped stochastic nonlinear Schrödinger equation. Zbl 1091.60010
Debussche, Arnaud; Odasso, Cyril
30
2005
Existence of densities for stable-like driven SDEs with Hölder continuous coefficients. Zbl 1272.60032
Debussche, Arnaud; Fournier, Nicolas
30
2013
Optimal control of a stochastic heat equation with boundary-noise and boundary-control. Zbl 1123.60052
Debussche, Arnaud; Fuhrman, Marco; Tessitore, Gianmario
29
2007
A regularity result for quasilinear stochastic partial differential equations of parabolic type. Zbl 1327.60124
Debussche, Arnaud; de Moor, Sylvain; Hofmanová, Martina
29
2015
A density perturbation method to study the eigenstructure of two-phase flow equation systems. Zbl 0917.76047
Cortes, Julien; Debussche, A.; Toumi, I.
25
1998
Ergodic BSDEs under weak dissipative assumptions. Zbl 1221.60080
Debussche, Arnaud; Hu, Ying; Tessitore, Gianmario
25
2011
Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections. Zbl 1233.60036
Debussche, Arnaud; Goudenège, Ludovic
24
2011
The dynamics of nonlinear reaction-diffusion equations with small Lévy noise. Zbl 1321.60004
Debussche, Arnaud; Högele, Michael; Imkeller, Peter
24
2013
The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows. Zbl 0838.76060
Debussche, A.; Dubois, T.; Temam, Roger
23
1995
Some properties of invariant measures of non symmetric dissipative stochastic systems. Zbl 1087.60049
Da Prato, Giuseppe; Debussche, Arnaud; Goldys, Beniamin
23
2002
Construction of stochastic inertial manifolds using backward integration. Zbl 0876.60040
Da Prato, Giuseppe; Debussche, Arnaud
22
1996
On the construction of families of approximate inertial manifolds. Zbl 0760.34050
Debussche, A.; Marion, M.
22
1992
2D stochastic Navier-Stokes equations with a time-periodic forcing term. Zbl 1154.35099
Da Prato, Giuseppe; Debussche, Arnaud
22
2008
Modified energy for split-step methods applied to the linear Schrödinger equation. Zbl 1209.65137
Debussche, Arnaud; Faou, Erwan
22
2009
Weak backward error analysis for SDEs. Zbl 1256.65002
Debussche, Arnaud; Faou, Erwan
22
2012
The Schrödinger equation with spatial white noise potential. Zbl 1387.60097
Debussche, Arnaud; Weber, Hendrik
19
2018
Convergent families of approximate inertial manifolds. Zbl 0836.35063
Debussche, A.; Temam, R.
17
1994
Control of the stochastic Burgers model of turbulence. Zbl 1111.49302
Da Prato, Giuseppe; Debussche, Arnaud
17
1999
Some new generalizations of inertial manifolds. Zbl 0948.35018
Debussche, A.; Temam, R.
17
1996
\(m\)-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise. Zbl 1119.35128
Da Prato, Giuseppe; Debussche, Arnaud
17
2007
Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise. Zbl 1452.76193
Debussche, Arnaud; Romito, Marco
17
2014
Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation. Zbl 1418.60069
Cerrai, Sandra; Debussche, Arnaud
17
2019
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient. Zbl 1428.60089
Bréhier, Charles-Edouard; Debussche, Arnaud
17
2018
Quasilinear generalized parabolic Anderson model equation. Zbl 1448.35320
Bailleul, I.; Debussche, A.; Hofmanová, M.
16
2019
A singular perturbation of the Cahn-Hilliard equation. Zbl 0741.35023
Debussche, Arnaud
15
1991
On the qualitative behaviour of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point. Zbl 0770.35027
Alouges, François; Debussche, Arnaud
15
1991
Dynamic programming for the stochastic Navier-Stokes equations. Zbl 0953.76016
da Prato, Giuseppe; Debussche, Arnaud
15
2000
Periodic solutions of the Korteweg–de Vries equation driven by white noise. Zbl 1075.35121
De Bouard, A.; Debussche, A.; Tsutsumi, Y.
15
2004
Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion. Zbl 1314.35159
Belaouar, Radoin; de Bouard, Anne; Debussche, Arnaud
15
2015
Random modulation of solitons for the stochastic Korteweg-de Vries equation. Zbl 1158.60359
de Bouard, A.; Debussche, A.
14
2007
Weak truncation error estimates for elliptic PDEs with lognormal coefficients. Zbl 1273.65166
Charrier, Julia; Debussche, Arnaud
14
2013
Small noise asymptotic of the timing jitter in soliton transmission. Zbl 1147.60041
Debussche, Arnaud; Gautier, Eric
13
2008
Inertial manifolds and the slow manifolds in meteorology. Zbl 0753.35043
Debussche, A.; Temam, R.
12
1991
The Korteweg-de Vries equation with multiplicative homogeneous noise. Zbl 1137.35086
de Bouard, Anne; Debussche, Arnaud
12
2007
Solution to the stochastic Schrödinger equation on the full space. Zbl 1407.35236
Debussche, Arnaud; Martin, Jörg
12
2019
Diffusion limit for a stochastic kinetic problem. Zbl 1267.35022
Debussche, Arnaud; Vovelle, Julien
12
2012
Differentiability of the transition semigroup of the stochastic Burgers equations, and application to the corresponding Hamilton-Jacobi equation. Zbl 0931.37036
Da Prato, Giuseppe; Debussche, Arnaud
11
1998
Numerical study of two-dimensional stochastic NLS equations. Zbl 1077.65006
Barton-Smith, Marc; Debussche, Arnaud; Di Menza, Laurent
11
2005
Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises. Zbl 1303.60051
Albeverio, Sergio; Debussche, Arnaud; Xu, Lihu
11
2012
Convergence of a semi-discrete scheme for the stochastic Korteweg-de Vries equation. Zbl 1132.35076
Debussche, Arnaud; Printems, Jacques
9
2006
Dynamic programming for the stochastic Burgers equation. Zbl 1016.49024
Da Prato, Giuseppe; Debussche, Arnaud
8
2000
Numerical resolution of stochastic focusing NLS equations. Zbl 1001.65006
Debussche, A.; Di Menza, L.
8
2002
On the martingale problem associated to the 2D and 3D stochastic Navier-Stokes equations. Zbl 1194.76033
Da Prato, Giuseppe; Debussche, Arnaud
8
2008
A modified Kardar-Parisi-Zhang model. Zbl 1136.60043
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
8
2007
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise. Zbl 1185.35222
de Bouard, Anne; Debussche, Arnaud
8
2009
The 2D-Navier-Stokes equations perturbed by a delta correlated noise. Zbl 1067.76023
Debussche, A.
8
2003
The Kolmogorov equation associated to the stochastic Navier-Stokes equations in 2D. Zbl 1085.60041
Barbu, Viorel; Da Prato, Giuseppe; Debussche, Arnaud
8
2004
Essential \(m\)-dissipativity of Kolmogorov operators corresponding to periodic 2D-Navier Stokes equations. Zbl 1096.35126
Da Prato, Giuseppe; Barbu, Viorel; Debussche, Arnaud
8
2004
Quasi-invariance of Gaussian measures transported by the cubic NLS with third-order dispersion on T. Zbl 1464.35317
Debussche, Arnaud; Tsutsumi, Yoshio
8
2021
Large deviations for the dynamic \(\phi ^{2n}_d\) model. Zbl 1422.60039
Cerrai, Sandra; Debussche, Arnaud
8
2019
Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation. Zbl 1038.60055
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
7
2004
Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations. Zbl 0989.65002
de Bouard, A.; Debussche, A.; Di Menza, L.
7
2001
Long-time behavior in scalar conservation laws. Zbl 1240.35352
Debussche, A.; Vovelle, J.
7
2009
Inertial manifolds and slow manifolds. Zbl 0723.58006
Debussche, A.; Temam, R.
6
1991
On a multilevel approach for the two-dimensional Navier-Stokes equations with finite elements. Zbl 0914.76049
Calgaro, C.; Debussche, A.; Laminie, J.
6
1998
An integral inequality for the invariant measure of a stochastic reaction-diffusion equation. Zbl 1364.60080
Da Prato, Giuseppe; Debussche, Arnaud
6
2017
Diffusion-approximation in stochastically forced kinetic equations. Zbl 1442.35286
Debussche, Arnaud; Vovelle, Julien
6
2021
Estimate for \(P_{t}D\) for the stochastic Burgers equation. Zbl 1350.60057
Da Prato, Giuseppe; Debussche, Arnaud
6
2016
Inertial manifolds with delay. Zbl 0822.34041
Debussche, A.; Temam, R.
5
1995
Absolute continuity of the invariant measures for some stochastic PDEs. Zbl 1157.60333
Da Prato, Giuseppe; Debussche, Arnaud
5
2004
A dynamical multi-level scheme for the Burgers equation: Wavelet and hierarchical finite element. Zbl 1087.76063
Debussche, A.; Laminie, J.; Zahrouni, E.
5
2005
On the discretization of a partial differential equation in the neighborhood of a periodic orbit. Zbl 0791.65071
Alouges, François; Debussche, Arnaud
5
1993
Approximation of exponential order of the attractor of a turbulent flow. Zbl 0814.76030
Debussche, A.; Dubois, T.
5
1994
Diffusion limit for the radiative transfer equation perturbed by a Markovian process. Zbl 1344.35148
Debussche, A.; De Moor, S.; Vovelle, J.
5
2016
Diffusion limit for the radiative transfer equation perturbed by a Wiener process. Zbl 1333.35295
Debussche, Arnaud; De Moor, Sylvain; Vovelle, Julien
5
2015
Inertial manifolds and Sacker’s equation. Zbl 0731.58057
Debussche, Arnaud
4
1990
Coupling for some partial differential equations driven by white noise. Zbl 1079.60061
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
4
2005
A consistent stochastic large-scale representation of the Navier-Stokes equations. Zbl 1506.76024
Debussche, Arnaud; Hug, Berenger; Mémin, Etienne
1
2023
Existence of martingale solutions for stochastic flocking models with local alignment. Zbl 1499.92160
Debussche, Arnaud; Rosello, Angelo
1
2022
Quasi-invariance of Gaussian measures transported by the cubic NLS with third-order dispersion on T. Zbl 1464.35317
Debussche, Arnaud; Tsutsumi, Yoshio
8
2021
Diffusion-approximation in stochastically forced kinetic equations. Zbl 1442.35286
Debussche, Arnaud; Vovelle, Julien
6
2021
Diffusion-approximation for a kinetic spray-like system with random forcing. Zbl 1487.60121
Debussche, Arnaud; Rosello, Angelo; Vovelle, Julien
2
2021
A piecewise deterministic limit for a multiscale stochastic spatial gene network. Zbl 1486.92065
Debussche, Arnaud; Nguepedja Nankep, Mac Jugal
1
2021
Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation. Zbl 1418.60069
Cerrai, Sandra; Debussche, Arnaud
17
2019
Quasilinear generalized parabolic Anderson model equation. Zbl 1448.35320
Bailleul, I.; Debussche, A.; Hofmanová, M.
16
2019
Solution to the stochastic Schrödinger equation on the full space. Zbl 1407.35236
Debussche, Arnaud; Martin, Jörg
12
2019
Large deviations for the dynamic \(\phi ^{2n}_d\) model. Zbl 1422.60039
Cerrai, Sandra; Debussche, Arnaud
8
2019
The Schrödinger equation with spatial white noise potential. Zbl 1387.60097
Debussche, Arnaud; Weber, Hendrik
19
2018
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient. Zbl 1428.60089
Bréhier, Charles-Edouard; Debussche, Arnaud
17
2018
Long time behavior of Gross-Pitaevskii equation at positive temperature. Zbl 1406.35376
de Bouard, Anne; Debussche, Arnaud; Fukuizumi, Reika
4
2018
An integral inequality for the invariant measure of a stochastic reaction-diffusion equation. Zbl 1364.60080
Da Prato, Giuseppe; Debussche, Arnaud
6
2017
Degenerate parabolic stochastic partial differential equations: quasilinear case. Zbl 1346.60094
Debussche, Arnaud; Hofmanová, Martina; Vovelle, Julien
63
2016
Estimate for \(P_{t}D\) for the stochastic Burgers equation. Zbl 1350.60057
Da Prato, Giuseppe; Debussche, Arnaud
6
2016
Diffusion limit for the radiative transfer equation perturbed by a Markovian process. Zbl 1344.35148
Debussche, A.; De Moor, S.; Vovelle, J.
5
2016
Invariant measure of scalar first-order conservation laws with stochastic forcing. Zbl 1331.60117
Debussche, A.; Vovelle, J.
34
2015
A regularity result for quasilinear stochastic partial differential equations of parabolic type. Zbl 1327.60124
Debussche, Arnaud; de Moor, Sylvain; Hofmanová, Martina
29
2015
Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion. Zbl 1314.35159
Belaouar, Radoin; de Bouard, Anne; Debussche, Arnaud
15
2015
Diffusion limit for the radiative transfer equation perturbed by a Wiener process. Zbl 1333.35295
Debussche, Arnaud; De Moor, Sylvain; Vovelle, Julien
5
2015
Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise. Zbl 1452.76193
Debussche, Arnaud; Romito, Marco
17
2014
Ergodicity results for the stochastic Navier-Stokes equations: an introduction. Zbl 1301.35086
Debussche, Arnaud
44
2013
Existence of densities for stable-like driven SDEs with Hölder continuous coefficients. Zbl 1272.60032
Debussche, Arnaud; Fournier, Nicolas
30
2013
The dynamics of nonlinear reaction-diffusion equations with small Lévy noise. Zbl 1321.60004
Debussche, Arnaud; Högele, Michael; Imkeller, Peter
24
2013
Weak truncation error estimates for elliptic PDEs with lognormal coefficients. Zbl 1273.65166
Charrier, Julia; Debussche, Arnaud
14
2013
Convergence of stochastic gene networks to hybrid piecewise deterministic processes. Zbl 1261.60073
Crudu, A.; Debussche, A.; Muller, A.; Radulescu, O.
51
2012
Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise. Zbl 1246.35194
Debussche, A.; Glatt-Holtz, N.; Temam, R.; Ziane, M.
39
2012
Weak backward error analysis for SDEs. Zbl 1256.65002
Debussche, Arnaud; Faou, Erwan
22
2012
Diffusion limit for a stochastic kinetic problem. Zbl 1267.35022
Debussche, Arnaud; Vovelle, Julien
12
2012
Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises. Zbl 1303.60051
Albeverio, Sergio; Debussche, Arnaud; Xu, Lihu
11
2012
Local martingale and pathwise solutions for an abstract fluids model. Zbl 1230.60065
Debussche, Arnaud; Glatt-Holtz, Nathan; Temam, Roger
89
2011
Weak approximation of stochastic partial differential equations: the nonlinear case. Zbl 1217.65011
Debussche, Arnaud
49
2011
1D quintic nonlinear Schrödinger equation with white noise dispersion. Zbl 1234.35242
Debussche, Arnaud; Tsutsumi, Yoshio
32
2011
Ergodic BSDEs under weak dissipative assumptions. Zbl 1221.60080
Debussche, Arnaud; Hu, Ying; Tessitore, Gianmario
25
2011
Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections. Zbl 1233.60036
Debussche, Arnaud; Goudenège, Ludovic
24
2011
Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise. Zbl 1233.60037
Debussche, Arnaud; Hoegele, Michael; Imkeller, Peter
4
2011
Scalar conservation laws with stochastic forcing. Zbl 1200.60050
Debussche, A.; Vovelle, J.
100
2010
The nonlinear Schrödinger equation with white noise dispersion. Zbl 1193.35213
de Bouard, Anne; Debussche, Arnaud
34
2010
Asymptotic behavior of stochastic PDEs with random coefficients. Zbl 1213.37122
da Prato, Giuseppe; Debussche, Arnaud
2
2010
Weak order for the discretization of the stochastic heat equation. Zbl 1215.60043
Debussche, Arnaud; Printems, Jacques
49
2009
Modified energy for split-step methods applied to the linear Schrödinger equation. Zbl 1209.65137
Debussche, Arnaud; Faou, Erwan
22
2009
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise. Zbl 1185.35222
de Bouard, Anne; Debussche, Arnaud
8
2009
Long-time behavior in scalar conservation laws. Zbl 1240.35352
Debussche, A.; Vovelle, J.
7
2009
2D stochastic Navier-Stokes equations with a time-periodic forcing term. Zbl 1154.35099
Da Prato, Giuseppe; Debussche, Arnaud
22
2008
Small noise asymptotic of the timing jitter in soliton transmission. Zbl 1147.60041
Debussche, Arnaud; Gautier, Eric
13
2008
On the martingale problem associated to the 2D and 3D stochastic Navier-Stokes equations. Zbl 1194.76033
Da Prato, Giuseppe; Debussche, Arnaud
8
2008
On a stochastic Korteweg-de Vries equation with homogeneous noise. Zbl 1176.35165
de Bernard, Anne; Debussche, Arnaud
1
2008
Conservative stochastic Cahn-Hilliard equation with reflection. Zbl 1130.60068
Debussche, Arnaud; Zambotti, Lorenzo
30
2007
Optimal control of a stochastic heat equation with boundary-noise and boundary-control. Zbl 1123.60052
Debussche, Arnaud; Fuhrman, Marco; Tessitore, Gianmario
29
2007
\(m\)-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise. Zbl 1119.35128
Da Prato, Giuseppe; Debussche, Arnaud
17
2007
Random modulation of solitons for the stochastic Korteweg-de Vries equation. Zbl 1158.60359
de Bouard, A.; Debussche, A.
14
2007
The Korteweg-de Vries equation with multiplicative homogeneous noise. Zbl 1137.35086
de Bouard, Anne; Debussche, Arnaud
12
2007
A modified Kardar-Parisi-Zhang model. Zbl 1136.60043
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
8
2007
Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrödinger equation. Zbl 1109.60051
de Bouard, Anne; Debussche, Arnaud
38
2006
Markov solutions for the 3D stochastic Navier-Stokes equations with state dependent noise. Zbl 1110.35110
Debussche, Arnaud; Odasso, Cyril
35
2006
Convergence of a semi-discrete scheme for the stochastic Korteweg-de Vries equation. Zbl 1132.35076
Debussche, Arnaud; Printems, Jacques
9
2006
Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise. Zbl 1068.35191
de Bouard, Anne; Debussche, Arnaud
46
2005
Ergodicity for a weakly damped stochastic nonlinear Schrödinger equation. Zbl 1091.60010
Debussche, Arnaud; Odasso, Cyril
30
2005
Numerical study of two-dimensional stochastic NLS equations. Zbl 1077.65006
Barton-Smith, Marc; Debussche, Arnaud; Di Menza, Laurent
11
2005
A dynamical multi-level scheme for the Burgers equation: Wavelet and hierarchical finite element. Zbl 1087.76063
Debussche, A.; Laminie, J.; Zahrouni, E.
5
2005
Coupling for some partial differential equations driven by white noise. Zbl 1079.60061
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
4
2005
A semi-discrete scheme for the stochastic nonlinear Schrödinger equation. Zbl 1055.65008
de Bouard, A.; Debussche, A.
32
2004
Periodic solutions of the Korteweg–de Vries equation driven by white noise. Zbl 1075.35121
De Bouard, A.; Debussche, A.; Tsutsumi, Y.
15
2004
The Kolmogorov equation associated to the stochastic Navier-Stokes equations in 2D. Zbl 1085.60041
Barbu, Viorel; Da Prato, Giuseppe; Debussche, Arnaud
8
2004
Essential \(m\)-dissipativity of Kolmogorov operators corresponding to periodic 2D-Navier Stokes equations. Zbl 1096.35126
Da Prato, Giuseppe; Barbu, Viorel; Debussche, Arnaud
8
2004
Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation. Zbl 1038.60055
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
7
2004
Absolute continuity of the invariant measures for some stochastic PDEs. Zbl 1157.60333
Da Prato, Giuseppe; Debussche, Arnaud
5
2004
Strong solutions to the stochastic quantization equations. Zbl 1071.81070
Da Prato, Giuseppe; Debussche, Arnaud
139
2003
The stochastic nonlinear Schrödinger equation in \(H^1\). Zbl 1027.60065
de Bouard, A.; Debussche, A.
108
2003
Ergodicity for the 3D stochastic Navier-Stokes equations. Zbl 1109.60047
Da Prato, Giuseppe; Debussche, Arnaud
95
2003
The 2D-Navier-Stokes equations perturbed by a delta correlated noise. Zbl 1067.76023
Debussche, A.
8
2003
Two-dimensional Navier-Stokes equations driven by a space-time white noise. Zbl 1013.60051
Da Prato, Giuseppe; Debussche, Arnaud
113
2002
Numerical simulation of focusing stochastic nonlinear Schrödinger equations. Zbl 0988.35156
Debussche, Arnaud; Di Menza, Laurent
44
2002
On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation. Zbl 1008.35074
de Bouard, A.; Debussche, A.
38
2002
Some properties of invariant measures of non symmetric dissipative stochastic systems. Zbl 1087.60049
Da Prato, Giuseppe; Debussche, Arnaud; Goldys, Beniamin
23
2002
Numerical resolution of stochastic focusing NLS equations. Zbl 1001.65006
Debussche, A.; Di Menza, L.
8
2002
Finite-time blow-up in the additive supercritical stochastic nonlinear Schrödinger equation: The real noise case. Zbl 1017.35105
de Bouard, A.; Debussche, A.
3
2002
Effect of a localized random forcing term on the Korteweg-de Vries equation. Zbl 1032.35155
Debussche, Arnaud; Printems, Jacques
32
2001
Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations. Zbl 0989.65002
de Bouard, A.; Debussche, A.; Di Menza, L.
7
2001
Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations. Zbl 1005.35084
de Bouard, Anne; Debussche, Arnaud; Di Menza, Laurent
3
2001
Dynamic programming for the stochastic Navier-Stokes equations. Zbl 0953.76016
da Prato, Giuseppe; Debussche, Arnaud
15
2000
Dynamic programming for the stochastic Burgers equation. Zbl 1016.49024
Da Prato, Giuseppe; Debussche, Arnaud
8
2000
Maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation. Zbl 0978.60069
Da Prato, Giuseppe; Debussche, Arnaud
4
2000
A stochastic nonlinear Schrödinger equation with multiplicative noise. Zbl 0952.60061
de Bouard, A.; Debussche, A.
89
1999
White noise driven Korteweg-de Vries equation. Zbl 0952.60062
de Bouard, A.; Debussche, A.; Tsutsumi, Y.
68
1999
Numerical simulation of the stochastic Korteweg-de Vries equation. Zbl 0948.76038
Debussche, Arnaud; Printems, Jacques
63
1999
Control of the stochastic Burgers model of turbulence. Zbl 1111.49302
Da Prato, Giuseppe; Debussche, Arnaud
17
1999
On the stochastic Korteweg-de Vries equation. Zbl 0912.60074
de Bouard, A.; Debussche, A.
79
1998
Hausdorff dimension of a random invariant set. Zbl 0919.58044
Debussche, A.
61
1998
A density perturbation method to study the eigenstructure of two-phase flow equation systems. Zbl 0917.76047
Cortes, Julien; Debussche, A.; Toumi, I.
25
1998
Differentiability of the transition semigroup of the stochastic Burgers equations, and application to the corresponding Hamilton-Jacobi equation. Zbl 0931.37036
Da Prato, Giuseppe; Debussche, Arnaud
11
1998
On a multilevel approach for the two-dimensional Navier-Stokes equations with finite elements. Zbl 0914.76049
Calgaro, C.; Debussche, A.; Laminie, J.
6
1998
Random attractors. Zbl 0884.58064
Crauel, Hans; Debussche, Arnaud; Flandoli, Franco
525
1997
On the finite dimensionality of random attractors. Zbl 0888.60051
Debussche, A.
47
1997
Stochastic Cahn-Hilliard equation. Zbl 0838.60056
Da Prato, Giuseppe; Debussche, Arnaud
105
1996
Construction of stochastic inertial manifolds using backward integration. Zbl 0876.60040
Da Prato, Giuseppe; Debussche, Arnaud
22
1996
Some new generalizations of inertial manifolds. Zbl 0948.35018
Debussche, A.; Temam, R.
17
1996
On the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0831.35088
Debussche, Arnaud; Dettori, Lucia
74
1995
The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows. Zbl 0838.76060
Debussche, A.; Dubois, T.; Temam, Roger
23
1995
...and 12 more Documents
all top 5

Cited by 1,953 Authors

58 Debussche, Arnaud
49 Wang, Bixiang
39 Caraballo Garrido, Tomás
38 Guo, Boling
35 Röckner, Michael
34 Duan, Jinqiao
30 Flandoli, Franco
29 Temam, Roger Meyer
27 Da Prato, Giuseppe
27 Gao, Hongjun
26 Zhou, Shengfan
26 Zhu, RongChan
25 Hairer, Martin
25 Oh, Tadahiro
24 Langa, Jose’ Antonio
24 Li, Yangrong
24 Zhu, Xiang-Chan
23 Hong, Jialin
23 Zhao, Wenqiang
22 Gess, Benjamin
22 Hofmanová, Martina
21 Brzeźniak, Zdzisław
21 Huang, Jianhua
20 Lu, Kening
20 Mohan, Manil Thankamani
19 Dong, Zhao
19 Shu, Ji
18 Real Anguas, José
17 Blömker, Dirk
17 Glatt-Holtz, Nathan E.
17 Gu, Anhui
17 Jentzen, Arnulf
17 Kloeden, Peter Eris
17 Romito, Marco
17 Xie, Yingchao
16 Marín-Rubio, Pedro
16 Miranville, Alain M.
16 Robinson, James Cooper
15 Barbu, Viorel
15 Karlsen, Kenneth Hvistendahl
15 Razafimandimby, Paul André
15 Weber, Hendrik
15 Zhang, Deng
15 Zhang, Rangrang
14 Chen, Yong
14 Gubinelli, Massimiliano
14 Li, Dingshi
14 Wang, Renhai
14 Yamazaki, Kazuo
13 Cui, Jianbo
13 de Bouard, Anne
13 Ferrario, Benedetta
13 Tzvetkov, Nikolay
13 Wu, Jianglun
12 Högele, Michael Anton
12 Vallet, Guy
12 Wang, Zhaojuan
12 You, Bo
12 Zhou, Guoli
11 Albeverio, Sergio A.
11 Cui, Hongyong
11 Hausenblas, Erika
11 Larsson, Stig
11 Luo, Dejun
11 Schmalfuß, Björn
11 Yang, Desheng
10 Anguiano, María
10 Bréhier, Charles-Edouard
10 Grasselli, Maurizio
10 Guo, Chunxiao
10 Guo, Yanfeng
10 Lisei, Hannelore
10 Shi, Lin
10 Wang, Xiaohu
10 Zhang, Tusheng S.
9 Bauzet, Caroline
9 Crauel, Hans
9 Kinra, Kush
9 Kovács, Mihály
9 Lv, Guangying
9 Scarpa, Luca
9 Shen, Hao
9 Tang, Hao
9 Wang, Guolian
8 Breit, Dominic
8 Goreac, Dan
8 Ju, Xuewei
8 Maslowski, Bohdan
8 Neamţu, Alexandra
8 Valero, José
8 Vovelle, Julien
8 Wang, Wei
8 Wang, Xiaojie
8 Wei, Caimin
8 Xin, Jie
8 Xu, Weijun
8 Yang, Meihua
8 Zhai, Jianliang
8 Zhang, Jian
8 Zhang, Qiangheng
...and 1,853 more Authors
all top 5

Cited in 300 Serials

137 Journal of Differential Equations
82 Journal of Mathematical Analysis and Applications
74 Stochastic Processes and their Applications
73 Stochastic and Partial Differential Equations. Analysis and Computations
62 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
61 Discrete and Continuous Dynamical Systems. Series B
61 Stochastics and Dynamics
46 Journal of Mathematical Physics
42 Stochastic Analysis and Applications
36 Communications in Mathematical Physics
33 The Annals of Probability
33 Discrete and Continuous Dynamical Systems
32 Journal of Functional Analysis
31 Chaos, Solitons and Fractals
30 Probability Theory and Related Fields
28 Applied Mathematics and Optimization
26 Journal of Computational Physics
26 Applied Mathematics and Computation
26 Physica D
25 Journal of Scientific Computing
25 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
24 Communications on Pure and Applied Analysis
23 Journal of Statistical Physics
22 The Annals of Applied Probability
22 Journal of Dynamics and Differential Equations
22 Potential Analysis
21 NoDEA. Nonlinear Differential Equations and Applications
20 Nonlinearity
20 Applied Numerical Mathematics
18 Mathematics of Computation
18 Electronic Journal of Probability
18 Journal of Evolution Equations
17 Mathematical Methods in the Applied Sciences
17 SIAM Journal on Mathematical Analysis
17 Abstract and Applied Analysis
17 Nonlinear Analysis. Real World Applications
16 Archive for Rational Mechanics and Analysis
16 Transactions of the American Mathematical Society
15 ZAMP. Zeitschrift für angewandte Mathematik und Physik
15 SIAM Journal on Numerical Analysis
15 Discrete and Continuous Dynamical Systems. Series S
14 Computers & Mathematics with Applications
14 Journal of Computational and Applied Mathematics
14 Numerische Mathematik
14 SIAM Journal on Control and Optimization
14 Journal de Mathématiques Pures et Appliquées. Neuvième Série
14 Infinite Dimensional Analysis, Quantum Probability and Related Topics
13 Communications on Pure and Applied Mathematics
13 BIT
13 Journal of Theoretical Probability
12 Advances in Difference Equations
12 Science China. Mathematics
11 Computers and Fluids
11 Applied Mathematics Letters
11 Stochastics
10 Statistics & Probability Letters
10 Applied Mathematics and Mechanics. (English Edition)
10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
10 SIAM Journal on Scientific Computing
10 Journal of Difference Equations and Applications
10 Acta Mathematica Sinica. English Series
10 Communications in Nonlinear Science and Numerical Simulation
10 Boundary Value Problems
9 Applicable Analysis
9 Physics Letters. A
9 Journal of Nonlinear Science
9 Journal of Mathematical Fluid Mechanics
9 Dynamical Systems
9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
8 Comptes Rendus. Mathématique. Académie des Sciences, Paris
8 Journal of Hyperbolic Differential Equations
8 SIAM/ASA Journal on Uncertainty Quantification
7 Inventiones Mathematicae
7 Mathematische Nachrichten
7 Bulletin des Sciences Mathématiques
7 Journal of the European Mathematical Society (JEMS)
7 Evolution Equations and Control Theory
7 AIMS Mathematics
6 Computer Methods in Applied Mechanics and Engineering
6 Annali di Matematica Pura ed Applicata. Serie Quarta
6 Chinese Annals of Mathematics. Series B
6 Communications in Partial Differential Equations
6 Chaos
6 Frontiers of Mathematics in China
5 Journal of Mathematical Biology
5 Mathematics and Computers in Simulation
5 Acta Mathematicae Applicatae Sinica. English Series
5 Numerical Methods for Partial Differential Equations
5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
5 Mathematical Problems in Engineering
5 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
5 Journal of Inequalities and Applications
5 Communications in Contemporary Mathematics
5 Forum of Mathematics, Sigma
5 Open Mathematics
4 Czechoslovak Mathematical Journal
4 Numerical Functional Analysis and Optimization
4 Proceedings of the American Mathematical Society
4 RAIRO. Modélisation Mathématique et Analyse Numérique
...and 200 more Serials
all top 5

Cited in 46 Fields

1,586 Partial differential equations (35-XX)
1,401 Probability theory and stochastic processes (60-XX)
590 Dynamical systems and ergodic theory (37-XX)
369 Fluid mechanics (76-XX)
335 Numerical analysis (65-XX)
115 Ordinary differential equations (34-XX)
96 Statistical mechanics, structure of matter (82-XX)
77 Systems theory; control (93-XX)
76 Operator theory (47-XX)
68 Quantum theory (81-XX)
68 Biology and other natural sciences (92-XX)
61 Calculus of variations and optimal control; optimization (49-XX)
57 Geophysics (86-XX)
29 Real functions (26-XX)
27 Mechanics of deformable solids (74-XX)
22 Classical thermodynamics, heat transfer (80-XX)
20 Integral equations (45-XX)
18 Functional analysis (46-XX)
18 Global analysis, analysis on manifolds (58-XX)
15 Measure and integration (28-XX)
14 Mechanics of particles and systems (70-XX)
13 Statistics (62-XX)
11 Harmonic analysis on Euclidean spaces (42-XX)
11 Operations research, mathematical programming (90-XX)
10 Optics, electromagnetic theory (78-XX)
9 Computer science (68-XX)
9 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
8 Difference and functional equations (39-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
6 Potential theory (31-XX)
5 Approximations and expansions (41-XX)
4 Special functions (33-XX)
4 Integral transforms, operational calculus (44-XX)
4 Differential geometry (53-XX)
4 Astronomy and astrophysics (85-XX)
3 General and overarching topics; collections (00-XX)
3 Functions of a complex variable (30-XX)
2 Algebraic geometry (14-XX)
2 Associative rings and algebras (16-XX)
2 Manifolds and cell complexes (57-XX)
2 Relativity and gravitational theory (83-XX)
1 Combinatorics (05-XX)
1 Topological groups, Lie groups (22-XX)
1 Several complex variables and analytic spaces (32-XX)
1 General topology (54-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year