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首页> 外文期刊>Communications in Partial Differential Equations >Compactness, kinetic formulation, and entropies for a problem related to micromagnetics
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Compactness, kinetic formulation, and entropies for a problem related to micromagnetics

机译：与微磁学有关的问题的紧致性，动力学公式和熵

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We carry on the study of (Riviere T, Serfaty S. Limiting domain wall energy for a problem related to micromagnetics. Comm Pure Appl Math 2001;, 54(3):294-338.) on the asymptotics of a family of energy-functionals related to micromagnetics. We prove compactness for families of uniformly bounded energies releasing the LBP condition we had previously set. Such families converge to unit-valued divergence-free vector-fields that are tangent to the boundary of the domain, and we found in (Riviere T, Serfaty S. Limiting domain wall energy for a problem related to micromagnetics. Comm Pure Appl Math 2001; 54(3):294-338.) that the energy-functionals Gamma-converge to a limiting jump-energy of such configurations. We examine the behavior of certain truncated fields which serve to construct "entropies," and to provide an improved lower bound. We give a kinetic formulation of the problem, and show that the limiting divergence-free problem is supplemented, in the case of minimizers, with a sign condition which can in turn, using the kinetic formulation, be interpreted as an entropy condition that plays a role in uniqueness questions. [References: 14]
机译：我们继续研究（Riviere T，Serfaty S.限制与微磁学有关的问题的畴壁能量。CommPure Appl Math 2001 ;, 54（3）：294-338。）关于一个能量族的渐近性的研究，与微磁学有关的功能。我们证明了释放先前设定的LBP条件的均匀界能量族的紧致性。这样的族收敛到与域的边界相切的单位值的无散度矢量场，我们在（Riviere T，Serfaty S.Limiting domain wall energy for an micromagnetics。Comm Pure Appl Math 2001 ; 54（3）：294-338。），能量功能Gamma收敛到这种配置的极限跳跃能量。我们检查了某些截短字段的行为，这些字段用于构造“熵”并提供改进的下界。我们给出问题的动力学公式，并表明在极小值的情况下，用无穷大条件补充了一个符号条件，该符号条件又可以用该动力学公式解释为一个熵条件，该熵条件起着在唯一性问题中的角色。 [参考：14]

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