Interface motion by interface diffusion driven by bulk energy: Justification of a diffusive interface model
MetadataShow full item record
We construct an asymptotic solution of a system consisting of the partial differential equations of linear elasticity theory coupled with a degenerate parabolic equation, and show that when a regularity parameter tends to zero, this solution converges to a solution of a sharp interface model, which describes the phase interface in an elastically deformable solid moving by interface diffusion. Therefore, the coupled system can be used as diffusive interface model. Differently from diffusive interface models based on the Cahn-Hilliard equation, the interface diffusion is solely driven by the bulk energy, hence the Laplacian of the curvature is not part of the driving force. Also, no rescaling of the parabolic equation is necessary. Since the asymptotic solution does not solve the system exactly, the proof is formal. © Springer-Verlag 2010.
Showing items related by title, author, creator and subject.
A parallel Branch-and-Fix Coordination based matheuristic algorithm for solving large sized multistage stochastic mixed 0-1 problems Aldasoro U.; Escudero L.F.; Merino M.; Pérez G. (European Journal of Operational Research, 2016-08-26)A parallel matheuristic algorithm is presented as a spin-off from the exact Branch-and-Fix Coordination (BFC) algorithm for solving multistage stochastic mixed 0-1 problems. Some steps to guarantee the solution’s optimality ...
Korotov S.; Křížek M. (Applied Mathematics Letters, 2011-12-31)In this note we show how to generate and conformally refine nonobtuse tetrahedral meshes locally in the neighbourhood of a polygonal face or a polygonal interior interface of a three-dimensional domain. The technique ...
Karátson J.; Korotov S. (Computers and Mathematics with Applications, 2015-12-31)The discrete maximum principle (DMP) is an important measure of the qualitative reliability of the applied numerical scheme for elliptic problems. This paper starts with formulating simple sufficient conditions for the ...