Interacting phase fields yielding phase separation on surfaces

2024/06/21 by Lledos, Benjamin, Marziani, Roberta, Olbermann, Heiner
#49J45 #49Q20 #92C10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.15300

Abstract

In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on ℝⁿ defined by two coupled phase fields u,v. The first phase field u is the diffuse approximation of the interior of the membrane; the second phase field v is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of Γ-convergence for pairs of phase functions (u_ε,v_ε). As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy.

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