Sharp-interface limit of the Allen-Cahn action functional in one space dimension

DOI10.1007/s00526-005-0370-5zbMath1094.60044OpenAlexW2166999972MaRDI QIDQ2492655

Yoshihiro Tonegawa, Maria G. Reznikoff, Robert V. Kohn

Publication date: 14 June 2006

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2115/8556

zbMATH Keywords

stochastic partial differential equationsaction minimizationAllen-Cahn equationlarge deviation theoryGamma convergencesharp-interface limits

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Large deviations (60F10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items

Large deviations for the macroscopic motion of an interface ⋮ Action minimization and macroscopic interface motion under forced displacement ⋮ On the existence of solution for a Cahn-Hilliard/Allen-Cahn equation ⋮ Unnamed Item ⋮ Tunneling in two dimensions ⋮ Mathematical and numerical aspects of a phase-field approach to critical nuclei morphology in solids ⋮ Large deviations approach to a one-dimensional, time-periodic stochastic model of pattern formation ⋮ Bifurcation of solutions to the Allen–Cahn equation ⋮ The variational problem for a certain space-time functional defined on planar closed curves ⋮ Action minimization for an Allen-Cahn equation with an unequal double-well potential ⋮ Large deviation principle for a stochastic Allen-Cahn equation ⋮ Stochastic Allen-Cahn approximation of the mean curvature flow: large deviations upper bound ⋮ Variational analysis of a mean curvature flow action functional

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