The Cauchy Problem for the Average Field Equation Describing a Model of a Magnetic Solid

V. Zh. Sakbaev

Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 434-445

Résumé

We study a model of a magnetic solid treated as a system of particles with mechanical moment $\vec s$, $\vec s\in S^2$, and magnetic moment $\vec\mu$, $\vec\mu =\vec s$, interacting with one another via the magnetic field, which determines variations in the mechanical moment of each particle. We study the system of integro-differential equations describing the evolution of the one-particle distribution function for this system of particles. We prove existence and uniqueness theorems for the generalized and the classical solution of the Cauchy problem for this system of equations. We also prove that the generalized solution continuously depends on the initial conditions.