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Dynamic boundary conditions in the interface modeling of binary alloys

1 Donetsk Institute for Physics and Engineering, Donetsk, 83114, Ukraine
2 Institute of Applied Mathematics and Mechanics of the NASU, Sloviansk, 84100, Ukraine
3 Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, 91711, USA

Topical Section: Mathematical Analysis in Fluid Dynamics

We study the initial boundary value problem with dynamic boundary conditions to thePenrose-Fife equations with a ‘memory e ect’ for the order parameter and temperature time evolutions.The dynamic boundary conditions describe the process of production and degradation of surfacecrystallite near the walls, which confine the disordered binary alloy at a nearly melt temperatureduring the fast cooling process. The solid-liquid periodic distributions, which were obtained in 1Dcase, represent asymptotically periodic piecewise constant spatial-temporal impulses in a long timedynamics. It is confirmed that, depending on parameter values, the total number of discontinuity pointsof such periodic impulses can be finite or infinite. We refer to such wave solution types as relaxationor pre-turbulent, respectively. These results are compared with experimental data.
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Keywords phase-field equations; di erence equations; pre-turbulent; turbulent; global attractor

Citation: Igor B. Krasnyuk, Roman M. Taranets, Marina Chugunova. Dynamic boundary conditions in the interface modeling of binary alloys. AIMS Mathematics, 2018, 3(3): 409-425. doi: 10.3934/Math.2018.3.409

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