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In this note, we consider a nonlinear diffusion equation with a bistable reaction term
arising in population dynamics. Given a rather general initial data, we investigate its
behavior for small times as the reaction coefficient tends to infinity: we prove a
generation of interface property.
Global existence of solutions for equations describing a motion of magnetohydrodynamic compresible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. We have proved that the domain occupied by the fluid remains close to the initial domain for all time.
We deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations.
We restrict our analysis to the case of a cylindrical symmetry for the crystal under study, so that the mathematical formulation will involve a two-dimensional variational problem.
The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so-called core region. We show that the -limit of this
energy (suitably rescaled),...
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