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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 17
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Research Article

Some problems related to nonlinear 3D-magnetoelasticity

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Pages 6028-6041 | Received 12 Jan 2021, Accepted 04 Apr 2021, Published online: 20 Apr 2021
 

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 α(t) in the elastic force α(t)β(x,t) acting on the body when some additional measurement is available.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the authors.

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