Phase Transition of Parabolic Ginzburg--Landau Equation with Potentials of High-Dimensional Wells

2022/07/26 by Yuning Liu, Liu, Yuning · 1 citation
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2207.12912

openalex publication_date 2022/07/26 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

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(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.

Cited by

• Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation

Related

• Phase transition of anisotropic Ginzburg--Landau equation
• Structural descriptions of limits of the parabolic Ginzburg-Landau equation on closed manifolds
• Hydrodynamic limit for the Ginzburg-Landau ∇ϕ interface model with non-convex potential
• Hydrodynamic limit for the Ginzburg-Landau ∇ϕ interface model with a conservation law and Dirichlet boundary conditions
• Harmonic maps in connection of phase transitions with higher dimensional potential wells