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Stability of microstructure for tetragonal to monoclinic martensitic transformations

Pavel Belik, Mitchell Luskin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to...

Stability results for convergence of convex sets and functions in nonreflexive spaces.

Jaafar Lahrache (1996)

Publicacions Matemàtiques

Let Γ(X) be the convex proper lower semicontinuous functions on a normed linear space X. We show, subject to Rockafellar’s constraints qualifications, that the operations of sum, episum and restriction are continuous with respect to the slice topology that reduces to the topology of Mosco convergence for reflexive X. We show also when X is complete that the epigraphical difference is continuous. These results are applied to convergence of convex sets.

Steady Boussinesq system with mixed boundary conditions including friction conditions

Tujin Kim (2022)

Applications of Mathematics

In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution...

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