RESEARCH ARTICLE
Phase transition of parabolic Ginzburg–Landau equation with potentials of high-dimensional wells
Yuning Liu,
Corresponding Author
Yuning Liu
NYU Shanghai, Shanghai, China
NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, Shanghai, China
Correspondence
Yuning Liu, NYU Shanghai, 567 Yangsi W road, Pudong, Shanghai 200126, China.
Email: [email protected]
Search for more papers by this authorYuning Liu,
Corresponding Author
Yuning Liu
NYU Shanghai, Shanghai, China
NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, Shanghai, China
Correspondence
Yuning Liu, NYU Shanghai, 567 Yangsi W road, Pudong, Shanghai 200126, China.
Email: [email protected]
Search for more papers by this authorFirst published: 27 January 2025
Abstract
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 (2012), no. 6, 833–888) 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.
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