Invariant measures of the stochastic LLB equation on R^2 are tight in H^1 for small noise and converge weakly to invariant measures of the deterministic limit equation.
N´ eel: Bases d’une nouvelle th´ eorie g´ en´ erale du champ coercitif, Ann
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Stability of invariant measures of the stochastic Landau-Lifshitz-Bloch equation with vanishing noise
Invariant measures of the stochastic LLB equation on R^2 are tight in H^1 for small noise and converge weakly to invariant measures of the deterministic limit equation.