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: MSRI: Simons Auditorium
35R15 - Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]
82D30 - Random media, disordered materials (including liquid crystals and spin glasses)
35R60 - Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]
82C31 - Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
35Qxx - Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]
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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