The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.
In this article we survey some of the most important developments since the 1980 paper of A.P. Calderón in which he proposed the problem of determining the conductivity of a medium by making voltage and current measurements at the boundary.
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...
In this paper, we continue the study of the Raman amplification in plasmas that we initiated in [Colin and Colin, Diff. Int. Eqs. 17 (2004) 297–330; Colin and Colin, J. Comput. Appl. Math. 193 (2006) 535–562]. We point out that the Raman instability gives rise to three components. The first one is collinear to the incident laser pulse and counter propagates. In 2-D, the two other ones make a non-zero angle with the initial pulse and propagate forward. Furthermore they are symmetric with respect...
In this paper, we continue the study of the Raman amplification in plasmas that we initiated in [Colin and Colin, Diff. Int. Eqs.17 (2004) 297–330; Colin and Colin, J. Comput. Appl. Math.193 (2006) 535–562]. We point out that the Raman instability gives rise to three components. The first one is collinear to the incident laser pulse and counter propagates. In 2-D, the two other ones make a non-zero angle with the initial pulse and propagate forward. Furthermore they are symmetric with respect to...
We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.