##### Department of Mathematics,

University of California San Diego

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### Special Seminar

## Michael Roeckner

#### Universität Bielefeld

## Self-organized criticality via stochastic partial differential equations

##### Abstract:

Models of self-organized criticality which can be described by stochastic partial differential equations with noncoercive mono- tone diffusivity function and multiplicative Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models) are analyzed. Existence and uniqueness of nonnegative strong solutions are proved. Previously numerically predicted transition to the critical state in 1-D is confirmed by a rigorous proof that this indeed happens in finite time with high probability.

Host: Bruce Driver

### June 24, 2008

### 10:00 AM

### AP&M 6402

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