Singular stochastic Allen-Cahn equations with dynamic boundary conditions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Orrieri, Carlo¹  Scarpa, Luca² 

[1] Sapienza Univ Roma, Dipartimento Matemat, Piazzale Aldo Moro 5, I-00185 Rome, Italy

[2] UCL, Dept Math, Gower St, London WC1E 6BT, England

关键词: Allen-Cahn equation;    Dynamic boundary conditions;    Singular potentials;    Well-posedness;    Asymptotic estimates;   

DOI  :  10.1016/j.jde.2018.10.007

来源: Elsevier

【 摘 要 】

We prove a well-posedness result for stochastic Allen-Cahn type equations in a bounded domain coupled with generic boundary conditions. The (nonlinear) flux at the boundary aims at describing the interactions with the hard walls and is motivated by some recent literature in physics. The singular character of the drift part allows for a large class of maximal monotone operators, generalizing the usual double-well potentials. One of the main novelties of the paper is the absence of any growth condition on the drift term of the evolution, neither on the domain nor on the boundary. A well-posedness result for variational solutions of the system is presented using a priori estimates as well as monotonicity and compactness techniques. A vanishing viscosity argument for the dynamic on the boundary is also presented. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free