Random dynamics of the stochastic Landau-Lifshitz-Bloch equation with colored noise in the real line

Abstract

In this paper, we are concerned the stochastic Landau-Lifshitz-Bloch equation driven by the colored noise, evolving in the entire real line. First, the well-posedness of strong solution is established using a domain expansion method. Then, we consider the existence and uniqueness of the pullback random attractors in regularity space $H^1\left(R\right)$. Finally, we prove the upper semi-continuity of the attractors as the noise coefficient α tending to zero. The uniform tail-ends estimates of solutions for overcoming the non-compactness difficulty of Sobolev embedding in unbounded domains and the energy method due to Ball are invoked to establish the asymptotic compactness of solutions.