A free-boundary problem modeling loop dislocations in crystals
The authors are dealing with the mathematical Berucki model studied numerically a loop dislocation whose shape is a torus generated by a rotation of a disc of unit radius about an axis. The rate of change of \(R(t)\), being the distance from the axis, is roughly given by the fluxes of intersticials and vacancies. The problem of the formation of dislocations is solved as a free-boundary problem for the torus. Some simplified problems are treated in one-, two- and three-dimensional cases. The existence and uniqueness theorems for their solutions are presented and proved. It is shown that there is a class of initial data for which the solution does not exist. A travelling wave solution is constructed and the complete three-dimensional problem with data close to it is concerned.
scientific article; zbMATH DE number 124150