论文标题
抛物线寄生虫 - 兰道等式的相变，具有高维井的电势
Phase Transition of Parabolic Ginzburg--Landau Equation with Potentials of High-Dimensional Wells
论文作者
论文摘要
在这项工作中，我们研究了具有高维井潜力的抛物线抛物线Ginzburg-Landau系统的共同维度界面限制和几何运动。主要结果概括了Lin等人。 （Comm。PureAppl。Math。，65（6）：833-888，2012）。特别是结合了调制能量方法和弱收敛方法，我们得出了内部和外部散装区域中的限制性谐波流动，而尖锐的界面则隔离了它们，并为它们提供了非标准的边界条件。这些结果是有效的，只要系统的初始数据在自然能量假设下得到充分准备就可以。
In this work, we study the co-dimensional one interface limit and geometric motions of parabolic Ginzburg--Landau systems with potentials of high-dimensional wells. The main result generalizes the one by Lin et al. (Comm. Pure Appl. Math., 65(6):833-888, 2012) to a dynamical case. In particular combining modulated energy methods and weak convergence methods, we derive the limiting harmonic heat flows in the inner and outer bulk regions segregated by the sharp interface, and a non-standard boundary condition for them. These results are valid provided that the initial datum of the system is well-prepared under natural energy assumptions.
