Communications in Mathematical Sciences

Volume 18 (2020)

Number 2

Existence of large solutions to the Landau–Lifshitz–Bloch equation

Pages: 487 – 513



Kamel Hamdache (Centre de recherche Académique, Pôle Universitaire Léonard de Vinci, Paris La Défense, France)

Djamila Hamroun (Laboratoire AMNEDP, Faculté de Mathématiques, Université des Sciences et Technologie Houari Boumediene (USTHB), Alger, Algeria)


In this work we discuss existence of solutions of the Landau–Lifshitz–Bloch equation describing the dynamics of the magnetization for the whole range of the temperature. By using energy method we prove global existence of strong solutions for given initial data, existence of time-periodic solutions as well as existence of steady state solutions of the equation.


Landau–Lifshitz–Bloch equation, magnetization, anisotropic energy, magnetostatic equations, regularization method, Galerkin approximation, fixed-point theorems

2010 Mathematics Subject Classification

35A01, 35G31, 35Q60, 82D40

Received 23 February 2018

Accepted 25 October 2019

Published 20 June 2022