A Magneto-Thermo-Elastic Identification Problem with a Moving Boundary in a Micro-Device

作者：Di Barba Paolo^*; Lorenzi Alfredo

来源：Milan Journal of Mathematics, 2013, 81(2): 347-383.

DOI：10.1007/s00032-013-0209-z

• magneto-thermal equations
• quasi static case
• identification problems
• existence and uniqueness of solutions
• systems of parabolic equations
• integro-differential parabolic equations

In this paper we model a thermally actuated device in the microdomain: a hollow metallic cylinder, coaxially located with respect to a current-carrying cable inside the cylinder is considered. Owing to induction heating, we have to deal with a (nonlinear) magneto-thermo-elastic problem with a moving boundary that we consider in the quasi static case. %26lt;br%26gt;Assuming that the intensity of the current is unknown, we have to solve an identification problem consisting of identifying the waveform of the electric current, when an additional information on the magnitude of the magnetic field is supplied on the inner face of the cylinder. %26lt;br%26gt;After setting our direct problem in the general form, we change it to a simpler, but handful, formulation. %26lt;br%26gt;Working in the class of classical Holder spaces, we can prove the existence and uniqueness of the solution to our identification problem.

• 出版日期2013-12