Pathwise numerics and dynamics of stochastic evolution equations

• Applicants: Professor Dr. Peter E. Kloeden; Professor Dr. Björn Schmalfuß
• Subject Area: Mathematics
• Term: from 2006 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 29324846

• Final Report Year: 2011

Final Report Abstract

No abstract available

Publications

• Qualitative behavior of a class of stochastic parabolic PDEs with dynamical boundary conditions. Discrete and Continuous Dynamical Systems - Series A, Vol. 18. 2007, Issue 2/3, pp. 315-338.
  I. Chueshov and B. Schmalfuß
  (See online at https://dx.doi.org/10.3934/dcds.2007.18.315)
• Random dynamics of the Boussinesq System with dynamical boundary conditions. Stochastic Analysis and Applications, Volume 27. 2009, Issue 5, pp. 1096-1116.
  P. Brune, J. Duan, and B. Schmalfuß
  (See online at https://dx.doi.org/10.1080/07362990902976546)
• Global attractor for a non-autonomous integro-differential equation in materials with memory. Nonlinear Analysis: Theory, Methods & Applications, Vol. 73. 2010, Issue 1, pp. 183–201.
  T. Caraballo, M.J. Garrido-Atienza, B. Schmalfuß and J. Valero.
  (See online at https://dx.doi.org/10.1016/j.na.2010.03.012)
• Random attractors for stochastic equations driven by a fractional Brownian motion. International Journal of Bifurcation and Chaos, Vol. 20. 2010, Issue 09, pp. 2761-2782.
  M.J. Garrido-Atienza, B. Maslowski, and B. Schmalfuß
  (See online at https://dx.doi.org/10.1142/S0218127410027349)
• Random dynamical systems for stochastic partial dierential equations driven by a fractional brownian motion. Discrete and Continuous Dynamical Systems, Series B, Vol. 14. 2010, Issue 2, pp. 473 - 493.
  Garrido-Atienza, K. Lu, and B. Schmalfuß
  (See online at https://dx.doi.org/10.3934/dcdsb.2010.14.473)
• Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion. Journal of Differential Equations, Vol. 248. 2010, Issue 7, pp. 1637–1667.
  Garrido-Atienza, K. Lu, and B. Schmalfuß
  (See online at https://dx.doi.org/10.1016/j.jde.2009.11.006)
• Ergodicity of the Infinite Dimensional Fractional Brownian Motion. J. Dynam. Dierential Equations, 2011. Accepted. Journal of Dynamics and Differential Equations, Vol. 23. 2011, Issue 3, pp 671-681.
  M.J. Garrido-Atienza and B. Schmalfuß
  (See online at https://dx.doi.org/10.1007/s10884-011-9222-5)
• Inertial manifolds for stochastic pde with dynamical Boundary conditions. Communications on Pure and Applied Analysis, Vol. 10. 2011, Issue 3, pp. 831-846.
  P. Brune and B. Schmalfuß
  (See online at https://dx.doi.org/10.3934/cpaa.2011.10.831)
• Random differential equations with random delays. Stochastics and Dynamics, Vol. 11. 2011, Issue 2, pp. 369-388.
  M.J. Garrido-Atienza, A. Ogrowsky, and B. Schmalfuß
  (See online at https://dx.doi.org/10.1142/S0219493711003358)