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1

Stochastic partial differential equations: analysis and computations

Arnaud Debussche, Boris Rozovsky

Journal:

Stochastic Partial Differential Equations: Analysis and Computations

Year:

2013

Language:

english

File:

PDF, 54 KB

english, 2013

2

Numerical methods for random and stochastic partial differential equations

Chernov, Alexey, Debussche, Arnaud, Nobile, Fabio

Journal:

Stochastic Partial Differential Equations: Analysis and Computations

Year:

2016

Language:

english

File:

PDF, 296 KB

english, 2016

3

Random attractors

Hans Crauel, Arnaud Debussche, Franco Flandoli

Journal:

Journal of Dynamics and Differential Equations

Year:

1997

Language:

english

File:

PDF, 1.12 MB

english, 1997

4

A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type

Debussche, Arnaud, de Moor, Sylvain, Hofmanová, Martina

Journal:

SIAM Journal on Mathematical Analysis

Year:

2015

Language:

english

File:

PDF, 300 KB

english, 2015

5

Degenerate parabolic stochastic partial differential equations: Quasilinear case

Debussche, Arnaud, Hofmanová, Martina, Vovelle, Julien

Journal:

The Annals of Probability

Year:

2016

Language:

english

File:

PDF, 339 KB

english, 2016

6

Numerical simulation of the stochastic Korteweg–de Vries equation

Arnaud Debussche, Jacques Printems

Journal:

Physica D: Nonlinear Phenomena

Year:

1999

Language:

english

File:

PDF, 1.43 MB

english, 1999

7

Control of the Stochastic Burgers Model of Turbulence

Da Prato, Giuseppe, Debussche, Arnaud

Journal:

SIAM Journal on Control and Optimization

Year:

1999

Language:

english

File:

PDF, 457 KB

english, 1999

8

Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion

Belaouar, Radoin, de Bouard, Anne, Debussche, Arnaud

Journal:

Stochastic Partial Differential Equations: Analysis and Computations

Year:

2015

Language:

english

File:

PDF, 1.94 MB

english, 2015

9

Numerical study of two-dimensional stochastic NLS equations

Marc Barton-Smith, Arnaud Debussche, Laurent Di Menza

Journal:

Numerical Methods for Partial Differential Equations

Year:

2005

Language:

english

File:

PDF, 442 KB

english, 2005

10

Two-Dimensional Navier–Stokes Equations Driven by a Space–Time White Noise

Giuseppe Da Prato, Arnaud Debussche

Journal:

Journal of Functional Analysis

Year:

2002

Language:

english

File:

PDF, 247 KB

english, 2002

11

Stochastic Burgers' equation

Guiseppe Da Prato, Arnaud Debussche, Roger Temam

Journal:

Nonlinear Differential Equations and Applications NoDEA

Year:

1994

Language:

english

File:

PDF, 468 KB

english, 1994

12

Ergodicity for a weakly damped stochastic non-linear Schrödinger equation

Arnaud Debussche, Cyril Odasso

Journal:

Journal of Evolution Equations

Year:

2005

Language:

english

File:

PDF, 285 KB

english, 2005

13

2D Stochastic Navier–Stokes Equations with a Time-Periodic Forcing Term

Giuseppe Da Prato, Arnaud Debussche

Journal:

Journal of Dynamics and Differential Equations

Year:

2008

Language:

english

File:

PDF, 240 KB

english, 2008

14

Local martingale and pathwise solutions for an abstract fluids model

Arnaud Debussche, Nathan Glatt-Holtz, Roger Temam

Journal:

Physica D: Nonlinear Phenomena

Year:

2011

Language:

english

File:

PDF, 389 KB

english, 2011

15

Effect of a Localized Random Forcing Term on the Korteweg-De Vries Equation

Arnaud Debussche, Jacques Printems

Journal:

Journal of Computational Analysis and Applications

Year:

2001

Language:

english

File:

PDF, 388 KB

english, 2001

16

Modified Energy for Split-Step Methods Applied to the Linear Schrödinger Equation

Debussche, Arnaud, Faou, Erwan

Journal:

SIAM Journal on Numerical Analysis

Year:

2009

Language:

english

File:

PDF, 241 KB

english, 2009

17

Existence of densities for stable-like driven SDEʼs with Hölder continuous coefficients

Debussche, Arnaud, Fournier, Nicolas

Journal:

Journal of Functional Analysis

Year:

2013

Language:

english

File:

PDF, 235 KB

english, 2013

18

Construction of stochastic inertial manifolds using backward integration

Prato, Giuseppe Da, Debussche, Arnaud

Journal:

Stochastics An International Journal of Probability and Stochastic Processes

Year:

1996

Language:

english

File:

PDF, 1.00 MB

english, 1996

19

Strong Solutions to the Stochastic Quantization Equations

Giuseppe Da Prato and Arnaud Debussche

Journal:

The Annals of Probability

Year:

2003

Language:

english

File:

PDF, 946 KB

english, 2003

20

Weak approximation of stochastic partial differential equations: the nonlinear case

Debussche, Arnaud

Journal:

Mathematics of Computation

Year:

2010

Language:

english

File:

PDF, 545 KB

english, 2010

21

Optimal control of a stochastic heat equation with boundary-noise and boundary-control

Debussche, Arnaud, Fuhrman, Marco, Tessitore, Gianmario

Journal:

ESAIM Control Optimisation and Calculus of Variations

Year:

2007

Language:

english

File:

PDF, 333 KB

english, 2007

22

Blow-Up for the Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise

Anne de Bouard and Arnaud Debussche

Journal:

The Annals of Probability

Year:

2005

Language:

english

File:

PDF, 2.30 MB

english, 2005

23

Weak Order for the Discretization of the Stochastic Heat Equation

Arnaud Debussche and Jacques Printems

Journal:

Mathematics of Computation

Year:

2009

Language:

english

File:

PDF, 1.22 MB

english, 2009

24

Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise

de Bouard, Anne, Debussche, Arnaud

Journal:

Electronic Journal of Probability

Year:

2009

Language:

english

File:

PDF, 231 KB

english, 2009

25

Stochastic Cahn-Hilliard equation

Giuseppe Da Prato, Arnaud Debussche

Journal:

Nonlinear Analysis: Theory, Methods & Applications

Year:

1996

Language:

english

File:

PDF, 949 KB

english, 1996

26

Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn–Hilliard equation

Giuseppe Da Prato, Arnaud Debussche, Luciano Tubaro

Journal:

Annales de l'Institut Henri Poincare (B) Probability and Statistics

Year:

2004

File:

PDF, 233 KB

2004

27

The nonlinear Schrödinger equation with white noise dispersion

Anne de Bouard, Arnaud Debussche

Journal:

Journal of Functional Analysis

Year:

2010

Language:

english

File:

PDF, 230 KB

english, 2010

28

Coupling for some partial differential equations driven by white noise

Giuseppe Da Prato, Arnaud Debussche, Luciano Tubaro

Journal:

Stochastic Processes and their Applications

Year:

2005

Language:

english

File:

PDF, 324 KB

english, 2005

29

Ergodic BSDEs under weak dissipative assumptions

Arnaud Debussche, Ying Hu, Gianmario Tessitore

Journal:

Stochastic Processes and their Applications

Year:

2011

Language:

english

File:

PDF, 294 KB

english, 2011

30

Ergodicity for the 3D stochastic Navier–Stokes equations

Giuseppe Da Prato, Arnaud Debussche

Journal:

Journal de Mathématiques Pures et Appliquées

Year:

2003

File:

PDF, 445 KB

2003

31

Numerical simulation of focusing stochastic nonlinear Schrödinger equations

Arnaud Debussche, Laurent Di Menza

Journal:

Physica D: Nonlinear Phenomena

Year:

2002

Language:

english

File:

PDF, 563 KB

english, 2002

32

On the discretization of a partial differential equation in the neighborhood of a periodic orbit

François Alouges, Arnaud Debussche

Journal:

Numerische Mathematik

Year:

1993

Language:

english

File:

PDF, 1.24 MB

english, 1993

33

Dynamic programming for the stochastic burgers equation

Giuseppe Da Prato, Arnaud Debussche

Journal:

Annali di Matematica Pura ed Applicata (1923 -)

Year:

2000

Language:

english

File:

PDF, 1.18 MB

english, 2000

34

Markov solutions for the 3Dstochastic Navier–Stokes equations with state dependent noise

Arnaud Debussche, Cyril Odasso

Journal:

Journal of Evolution Equations

Year:

2006

Language:

english

File:

PDF, 175 KB

english, 2006

35

Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

Anne de Bouard, Arnaud Debussche

Journal:

Applied Mathematics & Optimization

Year:

2006

Language:

english

File:

PDF, 311 KB

english, 2006

36

Some properties of invariant measures of non symmetric dissipative stochastic systems

Giuseppe Da Prato, Arnaud Debussche, Beniamin Goldys

Journal:

Probability Theory and Related Fields

Year:

2002

Language:

english

File:

PDF, 179 KB

english, 2002

37

m-Dissipativity of Kolmogorov Operators Corresponding to Burgers Equations with Space-time White Noise

Giuseppe Da Prato, Arnaud Debussche

Journal:

Potential Analysis

Year:

2007

Language:

english

File:

PDF, 483 KB

english, 2007

38

On the Cahn-Hilliard equation with a logarithmic free energy

Arnaud Debussche, Lucia Dettori

Journal:

Nonlinear Analysis: Theory, Methods & Applications

Year:

1995

Language:

english

File:

PDF, 853 KB

english, 1995

39

Absolute Continuity of the Invariant Measures for Some Stochastic PDEs

Giuseppe Da Prato, Arnaud Debussche

Journal:

Journal of Statistical Physics

Year:

2004

Language:

english

File:

PDF, 141 KB

english, 2004

40

1D quintic nonlinear Schrödinger equation with white noise dispersion

Arnaud Debussche, Yoshio Tsutsumi

Journal:

Journal de Mathématiques Pures et Appliquées

Year:

2011

Language:

english

File:

PDF, 177 KB

english, 2011

41

Hybrid stochastic simplifications for multiscale gene networks

Alina Crudu, Arnaud Debussche, Ovidiu Radulescu

Journal:

BMC Systems Biology

Year:

2009

Language:

english

File:

PDF, 894 KB

english, 2009

42

Weak Backward Error Analysis for SDEs

Debussche, Arnaud, Faou, Erwan

Journal:

SIAM Journal on Numerical Analysis

Year:

2012

Language:

english

File:

PDF, 227 KB

english, 2012

43

Exponential Mixing of the 3D Stochastic Navier-Stokes Equations Driven by Mildly Degenerate Noises

Albeverio, Sergio, Debussche, Arnaud, Xu, Lihu

Journal:

Applied Mathematics & Optimization

Year:

2012

Language:

english

File:

PDF, 1.06 MB

english, 2012

44

Weak truncation error estimates for elliptic PDEs with lognormal coefficients

Julia Charrier, Arnaud Debussche

Journal:

Stochastic Partial Differential Equations: Analysis and Computations

Year:

2013

Language:

english

File:

PDF, 495 KB

english, 2013

45

Existence of densities for the 3D Navier–Stokes equations driven by Gaussian noise

Arnaud Debussche, Marco Romito

Journal:

Probability Theory and Related Fields

Year:

2014

Language:

english

File:

PDF, 293 KB

english, 2014

46

Stochastic Cahn–Hilliard Equation with Double Singular Nonlinearities and Two Reflections

Debussche, Arnaud, Goudenège, Ludovic

Journal:

SIAM Journal on Mathematical Analysis

Year:

2011

Language:

english

File:

PDF, 283 KB

english, 2011

47

On the qualitative behavior of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point

Alouges, François, Debussche, Arnaud

Journal:

Numerical Functional Analysis and Optimization

Year:

1991

Language:

english

File:

PDF, 1.40 MB

english, 1991

48

THE KOLMOGOROV EQUATION ASSOCIATED TO THE STOCHASTIC NAVIER–STOKES EQUATIONS IN 2D

BARBU, VIOREL, DA PRATO, GIUSEPPE, DEBUSSCHE, ARNAUD

Journal:

Infinite Dimensional Analysis Quantum Probability and Related Topics

Year:

2004

Language:

english

File:

PDF, 229 KB

english, 2004

49

Conservative Stochastic Cahn-Hilliard Equation with Reflection

Arnaud Debussche and Lorenzo Zambotti

Journal:

The Annals of Probability

Year:

2007

Language:

english

File:

PDF, 2.02 MB

english, 2007

50

Small Noise Asymptotic of the Timing Jitter in Soliton Transmission

Arnaud Debussche and Eric Gautier

Journal:

The Annals of Applied Probability

Year:

2008

Language:

english

File:

PDF, 2.19 MB

english, 2008

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