Dirk Blömker and Jonas M. Tölle
Singular limits for stochastic equations
Stochastics and Dynamics 23, 2350040 (2023)
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Dirk Blömker and Alexandra Neamţu
Amplitude equations for SPDEs driven by fractional additive noise with small hurst parameter
Stochastics and Dynamics 22, 2240013 (2022)
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Dirk Blömker, Claudia Schillings, Philipp Wacker and Simon Weissmann
Continuous time limit of the stochastic ensemble Kalman inversion: strong convergence analysis
SIAM Journal on Numerical Analysis 60, 3181-3215 (2022)
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Shenglan Yuan and Dirk Blömker
Modulation and amplitude equations on bounded domains for nonlinear SPDEs driven by cylindrical alpha-stable Lévy processes
SIAM Journal on Applied Dynamical Systems 21, 1748-1777 (2022)
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Shenglan Yuan, Dirk Blömker and Jinqiao Duan
Stochastic turbulence for Burgers equation driven by cylindrical Lévy process
Stochastics and Dynamics 22, 2240004 (2022)
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Wael W. Mohammed and Dirk Blömker
Fast-diffusion limit for reaction-diffusion equations with multiplicative noise
Journal of Mathematical Analysis and Applications 496, 124808 (2021)
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Luigi Amedeo Bianchi and Dirk Blömker
The impact of white noise on a supercritical bifurcation in the Swift–Hohenberg equation
Physica D: Nonlinear Phenomena 415, 132742 (2021)
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Dirk Blömker and Alexander Schindler
Stochastic Cahn–Hilliard equation in higher space dimensions: the motion of bubbles
Zeitschrift für angewandte Mathematik und Physik 71, 49 (2020)
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Dirk Blömker and Hongbo Fu
The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations
Nonlinearity 33, 3905-3927 (2020)
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Dirk Blömker
Book Review: D. Breit, E. Feireisl, M. Hofmanová: "Stochastically Forced Compressible Fluid Flows", de Gruyter, 2018, 330 pp.
Jahresbericht der Deutschen Mathematiker-Vereinigung 121, 303-306 (Springer Fachmedien: Wiesbaden, 2019)
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Luigi Amedeo Bianchi, Dirk Blömker and Guido Schneider
Modulation equation and SPDEs on unbounded domains
Communications in Mathematical Physics 371, 19-54 (2019)
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Dirk Blömker and Minoo Kamrani
Numerically computable a posteriori-bounds for the stochastic Allen–Cahn equation
BIT Numerical Mathematics 59, 647-673 (2019)
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Dirk Blömker, Giuseppe Cannizzaro and Marco Romito
Random initial conditions for semi-linear PDEs
Proceedings of the Royal Society of Edinburgh Section A: Mathematics 150, 1533-1565 (2019)
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Dirk Blömker and Christian Nolde
Rigorous a-posteriori analysis using numerical eigenvalue bounds in a surface growth model
Journal of Dynamics and Differential Equations 32, 1233-1247 (2019)
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Dirk Blömker, Claudia Schillings, Philipp Wacker and Simon Weissmann
Well posedness and convergence analysis of the ensemble Kalman inversion
Inverse Problems 35, 085007 (2019)
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Dirk Blömker, Claudia Schillings and Philipp Wacker
A Strongly Convergent Numerical Scheme from Ensemble Kalman Inversion
SIAM Journal on Numerical Analysis 56, 2537-2562 (2018)
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Dirk Blömker
Computable a-posteriori bounds for SPDEs
in: Mini-Workshop: Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions, ed. by Martin Hutzenthaler, Annika Lang, Lukasz Szpruch and Larisa Yaroslavtseva, (Oberwolfach Reports ; 9/2017) 461-462 (European Mathematical Publishing House: Zürich, 2018)
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Dimitra C. Antonopoulou, Dirk Blömker and Georgia D. Karali
The sharp interface limit for the stochastic Cahn–Hilliard equation
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54, 280-298 (2018)
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Luigi Amedeo Bianchi, Dirk Blömker and Guido Schneider
Modulation equation and SPDEs on unbounded domains
preprint (2017)
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Bakhtiyar Ghayebi, Seyed Mohammad Hosseini and Dirk Blömker
Numerical solution of the Burgers equation with Neumann boundary noise
Journal of Computational and Applied Mathematics 311, 148-164 (2017)
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Dirk Blömker and Minoo Kamrani
Numerically Computable A Posteriori-Bounds for stochastic Allen-Cahn equation
preprint (2017)
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Minoo Kamrani and Dirk Blömker
Pathwise convergence of a numerical method for stochastic partial differential equations with correlated noise and local Lipschitz condition
Journal of Computational and Applied Mathematics 323, 123-135 (2017)
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Luigi Amedeo Bianchi, Dirk Blömker and Philipp Wacker
Pattern size in Gaussian fields from spinodal decomposition
SIAM Journal on Applied Mathematics 77, 1292-1319 (2017)
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Dirk Blömker, Philipp Wacker and Thomas Wanner
Probabilistic estimates of the maximum norm of random Neumann Fourier series
Communications in Nonlinear Science and Numerical Simulation 47, 348-369 (2017)
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Christian Nolde and Dirk Blömker
Rigorous a-posteriori analysis using numerical eigenvalue bounds in a surface growth model
preprint (2017)
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Luigi Bianchi and Dirk Blömker
Stochastic modulation equations on unbounded domains
in: Proceedings of EQUADIFF 2017 Conference: Bratislava, July 24-28, 2017, ed. by Karol Mikula, Daniel Ševčovič and Jozef Urbán, 295-304 (Slovak University of Technology, Spektrum Stu Publishing: Bratislava, 2017)
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Luigi Amedeo Bianchi, Dirk Blömker and Meihua Yang
Additive noise destroys the random attractor close to bifurcation
Nonlinearity 29, 3934-3960 (2016)
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Dirk Blömker, Evelyn Sander and Thomas Wanner
Degenerate nucleation in the Cahn-Hilliard-Cook model
SIAM Journal on Applied Dynamical Systems 15, 459-494 (2016)
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Wael W. Mohammed and Dirk Blömker
Fast Diffusion Limit for Reaction-Diffusion Systems with Stochastic Neumann Boundary Conditions
SIAM Journal on Mathematical Analysis 48, 3547-3578 (2016)
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Wael W. Mohammed and Dirk Blömker
Fast-diffusion limit with large noise for systems of stochastic reaction-diffusion equations
Stochastic Analysis and Applications 34, 961-978 (2016)
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Luigi Amedeo Bianchi and Dirk Blömker
Modulation equation for SPDEs in unbounded domains with space–time white noise – linear theory
Stochastic Processes and their Applications 126, 3171-3201 (2016)
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Dimitra C. Antonopoulou, P. W. Bates, Dirk Blömker and Georgia D. Karali
Motion of a Droplet for the Stochastic Mass-Conserving Allen-Cahn Equation
SIAM Journal on Mathematical Analysis 48, 670-708 (2016)
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Dirk Blömker, Christian Nolde and James C. Robinson
Rigorous numerical verification of uniqueness and smoothness in a surface growth model
Journal of Mathematical Analysis and Applications 429, 311-325 (2015)
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Dirk Blömker and Marco Romito
Stochastic PDEs and lack of regularity: a surface growth equation with noise: existence, uniqueness, and blow-up
Jahresbericht der Deutschen Mathematiker-Vereinigung 117, 233-286 (2015)
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Konrad Klepel, Dirk Blömker and Wael W. Mohammed
Amplitude equation for the generalized Swift–Hohenberg equation with noise
Zeitschrift für angewandte Mathematik und Physik 65, 1107-1126 (2014)
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Wael W. Mohammed, Dirk Blömker and Konrad Klepel
Multi-scale analysis of SPDEs with degenerate additive noise
Journal of Evolution Equations 14, 273-298 (2014)
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Dirk Blömker, K. Law, A. M. Stuart and K. C. Zygalakis
Accuracy and stability of the continuous-time 3DVAR filter for the Navier–Stokes equation
Nonlinearity 26, 2193-2219 (2013)
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Dirk Blömker and Wael W. Mohammed
Amplitude equations for SPDEs with cubic nonlinearities
Stochastics 85, 181-215 (2013)
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Dirk Blömker, Minoo Kamrani and Seyed Mohammad Hosseini
Full discretization of the stochastic Burgers equation with correlated noise
IMA Journal of Numerical Analysis 33, 825-848 (2013)
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Dirk Blömker and Arnulf Jentzen
Galerkin Approximations for the Stochastic Burgers Equation
SIAM Journal on Numerical Analysis 51, 694-715 (2013)
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Dirk Blömker and Marco Romito
Local existence and uniqueness for a two-dimensional surface growth equation with space-time white noise
preprint (2013)
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Erschienen in Stochastic Analysis and Applications, 31, 6, S. 1049-1076, https://doi.org/10.1080/07362994.2013.829003

Dirk Blömker and Marco Romito
Local existence and uniqueness for a two-dimensional surface growth equation with space-time white noise
Stochastic Analysis and Applications 31, 1049-1076 (2013)
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Wael W. Mohammed, Dirk Blömker and Konrad Klepel
Modulation Equation for Stochastic Swift-Hohenberg Equation
SIAM Journal on Mathematical Analysis 45, 14-30 (2013)
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Minoo Kamrani and Dirk Blömker
Numerical Solution of Stochastic Partial Differential Equations with Correlated Noise
preprint (2013)
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Dimitra C. Antonopoulou, Dirk Blömker and Georgia D. Karali
Front Motion in the One-Dimensional Stochastic Cahn-Hilliard Equation
SIAM Journal on Mathematical Analysis 44, 3242-3280 (2012)
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Dirk Blömker, Minoo Kamrani and Seyed Mohammad Hosseini
Full discretization of stochastic burgers equation with correlated noise
preprint (2012)
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Erschienen in IMA Journal of Numerical Analysis, 33, 3, S. 825-848, https://doi.org/10.1093/imanum/drs035

Dirk Blömker and Marco Romito
Local existence and uniqueness in the largest critical space for a surface growth model
Nonlinear Differential Equations and Applications NoDEA 19, 365-381 (2012)
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Dirk Blömker, Wael W. Mohammed, Christian Nolde and Franz Wöhrl
Numerical study of amplitude equations for SPDEs with degenerate forcing
International Journal of Computer Mathematics 89, 2499-2516 (2012)
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Dirk Blömker
Stabilization due to additive noise
in: Interplay of Analysis and Probability in Physics, ed. by Wolfgang König, Peter Mörters, Mark Peletier and Johannes Zimmer, (Oberwolfach Reports ; 06/2012) 329-332 (European Mathematical Publishing House: Zürich, 2012)
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D. Blömker, K. J. H. Law, A. M. Stuart and K. C. Zygalakis
The 3DVAR filter for the Navier-Stokes equation: accuracy and stability in the limit of high-frequency observations
AIP Conference Proceedings 1479, 916 (2012)
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Dirk Blömker
Amplitude equations – natural slow-fast systems
in: Mini-Workshop: Dynamics of Stochastic Systems and their Approximation, ed. by Evelyn Buckwar, Barbara Gentz and Erika Hausenblas, (Oberwolfach Reports ; 40/2011) 2310-2312 (European Mathematical Publishing House: Zürich, 2011)
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Dirk Blömker and Wael W. Mohammed
Modulation Equation for Stochastic Swift-Hohenberg Equation
preprint (2011)
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Erschienen in SIAM Journal on Mathematical Analysis, 45, 1, S. 14-30, https://doi.org/10.1137/110846336

Dirk Blömker, Martin Hairer and Grigorios A. Pavliotis
Some remarks on stabilization by additive noise
in: Stochastic partial differential equations and applications, ed. by Giuseppe Da Prato and Luciano Tubaro, (Quaderni di Matematica ; 25) 37-50 (Aracne Editrice: Roma, 2011)
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Dirk Blömker and Wael W. Mohammed
Amplitude Equations for SPDEs with Cubic Nonlinearities
preprint (2010)
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Erschienen in Stochastics, 85, 2, S. 181-215, https://doi.org/10.1080/17442508.2011.624628

Dirk Blömker and Yongqian Han
Asymptotic compactness of stochastic complex Ginzburg-Landau equation on an unbounded domain
Stochastics and Dynamics 10, 613-636 (2010)
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Dirk Blömker, Bernhard Gawron and Thomas Wanner
Nucleation in the one-dimensional stochastic Cahn-Hilliard model
Discrete and Continuous Dynamical Systems 27, 25-52 (2010)
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Dirk Blömker and Wael W. Mohammed
Amplitude Equation for SPDEs with Quadratic Non-Linearities
Electronic Journal of Probability 14, 2527-2550 (2009)
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Dirk Blömker and Arnulf Jentzen
Galerkin approximations for the stochastic Burgers equation
preprint (2009)
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Erschienen in SIAM Journal on Numerical Analysis, 51, 1, S. 694-715, https://doi.org/10.1137/110845756

Dirk Blömker, Franco Flandoli and Marco Romito
Markovianity and ergodicity for a surface growth PDE
The Annals of Probability 37, 275-313 (2009)
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Dirk Blömker and Wei Wang
Qualitative properties of local random invariant manifolds for SPDEs with quadratic nonlinearity
Journal of Dynamics and Differential Equations 22, 677-695 (2009)
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Dirk Blömker and Marco Romito
Regularity and blow up in a surface growth model
Dynamics of Partial Differential Equations 6, 227-252 (2009)
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Dirk Blömker, Stanislaus Maier-Paape and Thomas Wanner
Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation
Transactions of the American Mathematical Society 360, 449-489 (2008)
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Dirk Blömker, Martin Hairer and Grigorios A. Pavliotis
Some Remarks on Stabilization by Additive Noise
preprint (2008)
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Dirk Blömker
Stabilization due to additive noise
in: Infinite Dimensional Random Dynamical Systems and Their Applications, ed. by Franco Flandoli, Peter Kloeden and Andrew Stuart, (Oberwolfach Reports ; 50/2008) 2821-2823 (European Mathematical Publishing House: Zürich, 2008)
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Dirk Blömker, M. Romito and R. Tribe
A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
Annales de l'Institut Henri Poincare (B) Probability and Statistics 43, 175-192 (2007)
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Dirk Blömker
Amplitude Equations for Stochastic Partial Differential Equations
(Interdisciplinary Mathematical Sciences ; 3) (World Scientific: Singapore [u.a.], 2007)
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Dirk Blömker, M. Hairer and G. A. Pavliotis
Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities
Nonlinearity 20, 1721-1744 (2007)
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Dirk Blömker and Jinqiao Duan
Predictability of the Burgers Dynamics Under Model Uncertainty
in: Stochastic Differential Equations: Theory and Applications: A Volume in Honor of Professor Boris L Rozovskii, ed. by Peter H. Baxendale and Sergey V. Lototsky, (Interdisciplinary Mathematical Sciences ; 2) 71-89 (World Scientific: Singapore [u.a.], 2007)
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Dirk Blömker and Martin Hairer
Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures
in: Probability and Partial Differential Equations in Modern Applied Mathematics, ed. by Edward C. Waymire and Jinqiao Duan, (The IMA Volumes in Mathematics and its Applications ; 140) 41-59 (Springer: New York [u.a.], 2005)
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Dirk Blömker
Approximation of the stochastic Rayleigh-Bénard problem near the onset of convection and related problems
Stochastics and Dynamics 5, 441-474 (2005)
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Dirk Blömker, M. Hairer and G. A. Pavliotis
Modulation Equations: Stochastic Bifurcation in Large Domains
Communications in Mathematical Physics 258, 479-512 (2005)
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Dirk Blömker
Nonhomogeneous Noise and Q-Wiener Processes on Bounded Domains
Stochastic Analysis and Applications 23, 255-273 (2005)
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Dirk Blömker, Stanislaus Maier-Paape and Thomas Wanner
Phase separation in stochastic Cahn-Hilliard models
in: Mathematical methods and models in phase transitions, ed. by Alain Miranville, 1-42 (Nova Science Publishers: New York, 2005)
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Dirk Blömker, Martin Hairer and Greg A. Pavliotis
Stochastic Modulation Equations
PAMM 5, 611-612 (2005)
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Dirk Blömker, Martin Hairer and Grigorios A. Pavliotis
Stochastic Swift-Hohenberg equation near a change of stability
in: Proceedings of Equadiff 11 International Conference on Differential Equations: Czecho-Slovak series, Bratislava, July 25-29, 2005; [Part 2] Minisymposia and contributed talks, ed. by Marek Fila, A. Handlovičová, K. Mikula, Milan Medveď, Pavol Quittner and Daniel Ševčovič, 27-37 (Comenius University Press: Bratislava, 2005)
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H. Hadinejad-Mahram, D. Dahlhaus and Dirk Blömker
Matched-Filter Bound for Binary Signaling Over Dispersive Fading Channels With Receive Diversity
IEEE Transactions on Communications 52, 2082-2086 (2004)
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Dirk Blömker and Martin Hairer
Multiscale Expansion of Invariant Measures for SPDEs
Communications in Mathematical Physics 251, 515-555 (2004)
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Dirk Blömker and Martin Hairer
Stationary Solutions for a Model of Amorphous Thin-Film Growth
Stochastic Analysis and Applications 22, 903-922 (2004)
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Dirk Blömker and Christoph Gugg
Thin-Film-Growth-Models: On local solutions
in: Recent Developments in Stochastic Analysis and Related Topics: Proceedings of the First Sino-German Conference on Stochastic Analysis (A Satellite Conference of ICM 2002), ed. by Sergio Albeverio, Zhi-Ming Ma and Michael Roeckner, 66-77 (World Scientific: Singapore [u.a.], 2004)
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Dirk Blömker
Amplitude Equations for Locally Cubic Nonautonomous Nonlinearities
SIAM Journal on Applied Dynamical Systems 2, 464-486 (2003)
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Dirk Blömker and Stanislaus Maier-Paape
Pattern formation below criticality forced by noise
Zeitschrift für angewandte Mathematik und Physik 54, 1-25 (2003)
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Dirk Blömker, Jinqiao Duan and Thomas Wanner
Enstrophy dynamics of stochastically forced large-scale geophysical flows
Journal of Mathematical Physics 43, 2616 (2002)
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Dirk Blömker and Christoph Gugg
On the existence of solutions for amorphous molecular beam epitaxy
Nonlinear Analysis: Real World Applications 3, 61-73 (2002)
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Dirk Blömker, Christoph Gugg and Stanislaus Maier-Paape
Stochastic Navier–Stokes equation and renormalization group theory
Physica D: Nonlinear Phenomena 173, 137-152 (2002)
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Dirk Blömker, Christoph Gugg and Martin Raible
Thin-film-growth models: roughness and correlation functions
European Journal of Applied Mathematics 13, 385-402 (2002)
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Dirk Blömker, Stanislaus Maier-Paape and Thomas Wanner
Roughness in surface growth equations
Interfaces and Free Boundaries 3, 465-484 (2001)
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Dirk Blömker, Stanislaus Maier-Paape and Thomas Wanner
Spinodal Decomposition for the Cahn–Hilliard–Cook Equation
Communications in Mathematical Physics 223, 553-582 (2001)
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Dirk Blömker, Stanislaus Maier-Paape and Thomas Wanner
Surface roughness in molecular beam epitaxy
Stochastics and Dynamics 1, 239-260 (2001)
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G. Schneider, Stanislaus Maier-Paape and Dirk Blömker
The stochastic Landau equation as an amplitude equation
Discrete and Continuous Dynamical Systems - Series B 1, 527-541 (2001)
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Dirk Blömker, Stanislaus Maier-Paape and Thomas Wanner
Spinodal decomposition for the stochastic Cahn-Hilliard equation
in: Equadiff 99: Proceedings of the International Conference on Differential Equations, ed. by Bernold Fiedler, Konrad Gröger and Jürgen Sprekels, 1265-1267 (World Scientific: Singapore [u.a.], 2000)
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Dirk Blömker
Stochastic partial differential equations and surface growth
Dissertation, Universität Augsburg, (Augsburger mathematisch-naturwissenschaftliche Schriften ; 35) (Wißner: Augsburg, 2000)
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Zugl.: Augsburg, Univ., Diss., 2000