Global existence and uniqueness of smooth solution to Landau-Lifshitz-Bloch equation with potential function

Abstract The Landau-Lifshitz-Bloch equation is commonly used to characterize the micromagnetic phenomena near Curie temperature. In this paper, we first use the difference method to verify the local existence of smooth solutions for the Landau-Lifshitz-Bloch equations with potential functions. Then we use the energy method to verify the global existence and uniqueness of smooth solutions for periodic initial value problems as well as the Cauchy problem of the Landau-Lifshitz-Bloch equations in dimension one. Moreover, the approach adopted in this paper can be further extended to the investigation of the existence of solutions for other ferromagnetic chain equations