BOUNDARY CONTROL OF THE NUMBER OF INTERFACES FOR THE ONE-DIMENSIONAL ALLEN-CAHN EQUATION

Jean-Paul Chehab (1) , Alejandro A. Franco (2, 3, 4) , Youcef Mammeri (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 LRCS - Laboratoire réactivité et chimie des solides - UMR CNRS 7314
3 RS2E - Réseau sur le stockage électrochimique de l'énergie
4 ALISTORE-ERI - Advanced Lithium Energy Storage Systems - ALISTORE-ERI

The identification of optimal structures in reaction-diffusion models is of great importance in numerous physicochemical systems. We propose here a simple method to monitor the number of interphases formed after long simulated times by using a boundary flux condition as a control parameter. We consider as an illustration a 1-D Allen-Cahn equation with Neumann boundary conditions. Numerical examples are provided and perspectives for the application of this approach to electrochemical systems are discussed.

Domaines: Matériaux

Jean-Paul Chehab, Alejandro A. Franco, Youcef Mammeri. BOUNDARY CONTROL OF THE NUMBER OF INTERFACES FOR THE ONE-DIMENSIONAL ALLEN-CAHN EQUATION. Discrete and Continuous Dynamical Systems - Series S, 2017, 10 (1), pp.87-100. ⟨10.3934/dcdss.2017005⟩. ⟨hal-03611049⟩