Global solution to the Allen-Cahn equation with singular potentials and dynamic boundary conditions

From MaRDI portal
Publication:1934986

DOI10.1016/j.na.2012.11.010zbMath1270.35275arXiv1206.6738OpenAlexW2021587782MaRDI QIDQ1934986

Pierluigi Colli, Luca Calatroni

Publication date: 30 January 2013

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.6738




Related Items (max. 100)

A class of quasi-linear Allen-Cahn type equations with dynamic boundary conditionsA boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditionsAn efficient diffusion generated motion method for wetting dynamicsAsymptotic limits and optimal control for the Cahn-Hilliard system with convection and dynamic boundary conditionsWell-posedness for a phase-field transition system endowed with a polynomial nonlinearity and a general class of nonlinear dynamic boundary conditionsAnalysis of an iterative scheme of fractional steps type associated to the nonlinear phase-field equation with non-homogeneous dynamic boundary conditionsThe Cahn--Hilliard Equation with Forward-Backward Dynamic Boundary Condition via Vanishing ViscosityOptimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle PotentialsStability and errors analysis of two iterative schemes of fractional steps type associated to a nonlinear reaction-diffusion equationNull controllability for semilinear heat equation with dynamic boundary conditionsA structure-preserving scheme for the Allen-Cahn equation with a dynamic boundary conditionOn a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentialsLagrange multiplier and singular limit of double obstacle problems for the Allen-Cahn equation with constraintDistributed and boundary optimal control of the Allen–Cahn equation with regular potential and dynamic boundary conditionsCoupled Bulk-Surface Free Boundary Problems Arising from a Mathematical Model of Receptor-Ligand DynamicsA qualitative analysis of a second-order anisotropic phase-field transition system endowed with a general class of nonlinear dynamic boundary conditionsWell-posedness and optimal control for a viscous Cahn-Hilliard-Oono system with dynamic boundary conditionsSecond-order sufficient conditions for sparse optimal control of singular Allen-Cahn systems with dynamic boundary conditionsA note on regularity and separation for the stochastic Allen-Cahn equation with logarithmic potentialOptimal control for a phase field system with a possibly singular potentialA review on the Cahn-Hilliard equation: classical results and recent advances in dynamic boundary conditionsStochastic Allen-Cahn equation with logarithmic potentialGlobal Hessian estimates for an Allen-Cahn equation on Riemannian manifoldsVanishing diffusion in a dynamic boundary condition for the Cahn-Hilliard equationSingular stochastic Allen-Cahn equations with dynamic boundary conditionsEquation and dynamic boundary condition of Cahn-Hilliard type with singular potentialsHarnack inequalities for a class of heat flows with nonlinear reaction termsBoundary control of the number of interfaces for the one-dimensional Allen-Cahn equationOn the stochastic Cahn-Hilliard equation with a singular double-well potentialOn a Cahn-Hilliard system with convection and dynamic boundary conditionsOn the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potentialOn the longtime behavior of a viscous Cahn-Hilliard system with convection and dynamic boundary conditionsGlobal Existence for a Nonstandard Viscous Cahn--Hilliard System with Dynamic Boundary ConditionThe Allen-Cahn equation with dynamic boundary conditions and mass constraintsExistence and uniqueness of solutions to singular Cahn-Hilliard equations with nonlinear viscosity terms and dynamic boundary conditionsConvergence to equilibrium for a bulk-surface Allen-Cahn system coupled through a nonlinear Robin boundary conditionCahn-Hilliard equation on the boundary with bulk condition of Allen-Cahn typeOn a coupled bulk-surface Allen-Cahn system with an affine linear transmission condition and its approximation by a Robin boundary conditionConvergence of Cahn–Hilliard systems to the Stefan problem with dynamic boundary conditionsOn second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: well-posedness, regularity theory and eigenvalue problemsRandom separation property for stochastic Allen-Cahn-type equationsSurface, bulk, and geometric partial differential equations: interfacial, stochastic, non-local and discrete structures. Abstracts from the workshop held January 20--26, 2019Time periodic solutions of Cahn-Hilliard systems with dynamic boundary conditionsConvergence of a Robin boundary approximation for a Cahn–Hilliard system with dynamic boundary conditionsA Cahn-Hilliard system with forward-backward dynamic boundary condition and non-smooth potentialsA deep quench approach to the optimal control of an Allen-Cahn equation with dynamic boundary conditions and double obstaclesSeparation property and convergence to equilibrium for the equation and dynamic boundary condition of Cahn–Hilliard type with singular potentialBoundary control problem and optimality conditions for the Cahn–Hilliard equation with dynamic boundary conditionsCahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary




This page was built for publication: Global solution to the Allen-Cahn equation with singular potentials and dynamic boundary conditions