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Introduction to Stochastic Partial Differential Equations

Introductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations August 24, 2015 - August 28, 2015

August 25, 2015 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Arnaud Debussche (Ecole Normale Supérieure de Rennes)
Location: MSRI: Simons Auditorium
  • SPDEs involving white noise

  • Burger's equation

  • reaction-diffusion equation

  • Wick product

  • Fokker-Planck

  • global existence and uniqueness results

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



SPDEs with white noise. I will focus on the stochastic Burgers and reaction-diffusion equations which will be first solved with spatially smooth noise and then with space time white noise. The case of the reaction-diffusion equation in dimension 2 is already not so obvious since the solutions are not expected to be function valued processes. The case of dimension 3 is much more difficult and has been solved only recently by Martin Hairer. I will not explain in details his theory on regularity structure, this would take too much time. However, I will explain why the problem is so difficult and give few hints on this difficult theory. No prerequisite on stochastic calculus is expected from the audience.

24214?type=thumb Debussche Notes 599 KB application/pdf Download
Video/Audio Files


H.264 Video 14339.mp4 321 MB video/mp4 rtsp://videos.msri.org/data/000/024/092/original/14339.mp4 Download
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