A geometric condition for the uniform stability of linear magnetoelasticity

We give a necessary and sufficient condition, of geometrical type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is assumed. Our strategy is to use microlocal defect measures to show suitable observability inequalities on high-frequency solutions of the Lamé system.

Heat Transfer in Composite Spheroids

Heat transfer from a composite prolate spheroid under the third-type boundary condition is investigated using a Legendre series expansion. The model is verified against published data on cooling boiled eggs and also against the asymptotic solution of a composite sphere. The impact of Biot number on the heat transfer in spheroids with realistic dimensions and properties, such as eggs and olives, is investigated. The results are also presented for varying conductivity ratios and fractional volume of the inner part of the spheroid.

Neumann and Robin type boundary conditions in Fractional Orlicz-Sobolev spaces

In the first part of this article we deal with the existence of at least three non-trivial weak solutions of a nonlocal problem with nonstandard growth involving a nonlocal Robin type boundary condition. The second part of the article is devoted to study eigenvalues and minimizers of several nonlocal problems for the fractional $g-$Laplacian $(-\Delta_g)^s$ with different boundary conditions, namely, Dirichlet, Neumann and Robin.