The stochastic Landau-Lifshitz equation
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: SLMath: Eisenbud Auditorium
micro-magnetics
stochastic PDE
ferromagnetism
temperature
white noise
Gibbs measure
weak solutions
35L03 - Initial value problems for first-order hyperbolic equations
76F60 - $k$k-$\varepsilon$\varepsilon modeling in turbulence
35L35 - Initial-boundary value problems for higher-order hyperbolic equations
57R70 - Critical points and critical submanifolds in differential topology
60D05 - Geometric probability and stochastic geometry [See also 52A22, 53C65]
76E15 - Absolute and convective instability and stability in hydrodynamic stability
14392
We will review some recent results on the stochastic Landau-Lifshitz equation which models temperature effects on magnetization dynamics in micro-magnetism. The particularity of the model is the geometric constraint the magnetization is a unit vector — which makes the equation nonlinear. The associated stochastic partial differential equation, taking account of temperature effects, has known some recent improvements, from the point of view of mathematical analysis as well as numerical analysis, but still offers a lot of open problems
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14392
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