Some problems related to nonlinear 3D-magnetoelasticity

Abstract

We consider some direct and inverse problems associated with the vibration of an elastic conductive body governed by the Lamé and Maxwell equations coupled through the nonlinear magnetoelastic effect. First, we prove the existence and uniqueness result for a mixed initial-boundary value problem. Uniqueness is proved under additional assumptions on the smoothness of the solution. Second, we prove the solvability of an inverse problem, which consists of identifying the unknown scalar function $\alpha (t)$ in the elastic force $\alpha (t)\beta (\mathbf{x},t)$ acting on the body when some additional measurement is available.

Keywords:

• 3D-nonlinear magnetoelastic effect
• initial boundary value problem
• inverse source problem
• existence and uniqueness

2010 Mathematics Subject Classifications:

• 35M12
• 35R30
• 74F15

Disclosure statement

No potential conflict of interest was reported by the authors.