Introduction to Stochastic Partial Differential Equations
Introductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations August 24, 2015 - August 28, 2015
Location: SLMath: Eisenbud Auditorium
SPDEs involving white noise
Burger's equation
reaction-diffusion equation
Wick product
Fokker-Planck
global existence and uniqueness results
35K52 - Initial-boundary value problems for higher-order parabolic systems
37A35 - Entropy and other invariants, isomorphism, classification in ergodic theory
35B60 - Continuation and prolongation of solutions to PDEs [See also 58A15, 58A17, 58Hxx]
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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.
Debussche Notes
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14339
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