Mikhail Vishnevskii

On an initial boundary value problem in nonlinear 3D-magnetoelasticity

Abstract We prove existence and uniqueness of a weak solution to an initial boundary value problem, related to the Maxwell and Lame systems nonlinearly coupled through the so-called magnetoelastic effect. Uniqueness is proved under additional assumptions on the smoothness of the solution.

An evolution problem related to nonlinear 2d-magnetoelasticity

Abstract There is studied a two-dimensional initial–boundary-value problem for the Lame and Maxwell equations coupled through the nonlinear magnetoelastic effect. We prove the existence and uniqueness result.

An identification problem related to the Biot system

Abstract In this paper, we study the propagation of elastic waves in porous media governed by the Biot equations in the low frequency range. We prove the existence and uniqueness result both for the direct problem and the inverse one, which consists in identifying the unknown scalar function f(t) in the body density force f(t)𝐠(𝐱,t) acting on a poroelastic body when some additional measurement is available.