Upper Bounds for Coarsening for the Deep Quench Obstacle Problem |
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Authors: | Amy Novick-Cohen |
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Institution: | 1.Department of Mathematics,Technion-IIT,Haifa,Israel |
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Abstract: | The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and
low concentration are formed, then coarsen or grow in average size. Of interest is the time dependence of the dominant length scales of the system. Relying on recent
results by Novick-Cohen and Shishkov (Discrete Contin. Dyn. Syst. B 25:251–272, 2009), we demonstrate upper bounds for coarsening for the deep quench obstacle problem, with either constant or degenerate mobility.
For the case of constant mobility, we obtain upper bounds of the form t
1/3 at early times as well as at times t for which
E(t) £ \frac(1-`(u)]2)4E(t)\le\frac{(1-\overline{u}^{2})}{4}, where E(t) denotes the free energy. For the case of degenerate mobility, we get upper bounds of the form t
1/3 or t
1/4 at early times, depending on the value of E(0), as well as bounds of the form t
1/4 whenever
E(t) £ \frac(1-`(u)]2)4E(t)\le\frac{(1-\overline{u}^{2})}{4}. |
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Keywords: | |
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