Ginzburg-Landau equation and motion by mean curvature. II: Development of the initial interface

DOI10.1007/BF02921629zbMath0935.35061OpenAlexW1972038087MaRDI QIDQ1298382

Halil Mete Soner

Publication date: 24 April 2000

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921629

zbMATH Keywords

maximum principletraveling wavesasymptotic behavior of solutionsshort time behavior

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Singular perturbations in context of PDEs (35B25)

Related Items (17)

Interacting particle systems and generalized evolution of fronts ⋮ Motion of concentration sets in Ginzburg-Landau equations. ⋮ Exponentially slow dynamics and interfaces intersecting the boundary ⋮ Convergence of solutions of some Allen-Cahn equations to Brakke's mean curvature flow ⋮ On the convergence rate of a reaction-diffusion equation with chemotaxis to a viscosity solution ⋮ Mean curvature flow by the Allen–Cahn equation ⋮ Convergence of diffusion generated motion to motion by mean curvature ⋮ Weak regularity of Gauss mass transport ⋮ Convergence rate of the Allen-Cahn equation to generalized motion by mean curvature ⋮ Generation, propagation, and annihilation of metastable patterns ⋮ Strong solutions for an incompressible Navier-Stokes/Allen-Cahn system with different densities ⋮ On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions ⋮ Convergence of solutions of the weighted Allen-Cahn equations to Brakke type flow ⋮ Ginzburg-Landau equation and motion by mean curvature. I: Convergence ⋮ Convergence of the Allen--Cahn Equation with Neumann Boundary Conditions ⋮ Thermal capacity estimates on the Allen-Cahn equation ⋮ A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method

Cites Work

• Unnamed Item
• Generation and propagation of interfaces for reaction-diffusion equations
• Motion of a set by the curvature of its boundary
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
• Fast Reaction, Slow Diffusion, and Curve Shortening
• Phase transitions and generalized motion by mean curvature
• Front Propagation and Phase Field Theory
• Development of interfaces in ℝ^N

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