An inverse problem for the fractional Allen-Cahn equation

2025/08/15 by Li, Li
#35R11 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.11208

Abstract

We study an inverse problem for the fractional Allen-Cahn equation. Our formulation and arguments rely on the asymptotics for the fractional equation and unique continuation properties.

Citations

• Fractional multi-phase transitions and nonlocal minimal partitions
• Calderón problem for fractional Schrödinger operators on closed Riemannian manifolds
• An inverse problem for the fractionally damped wave equation
• Fractional anisotropic Calderón problem on closed Riemannian manifolds
• Stable solutions to the fractional Allen-Cahn equation in the nonlocal perimeter regime
• An Inverse Problem for Non-linear Fractional Magnetic Schrodinger Equation
• Inverse problems for fractional semilinear elliptic equations
• Asymptotics for the fractional Allen-Cahn equation and stationary nonlocal minimal surfaces
• Quantitative flatness results and BV-estimates for stable nonlocal\n minimal surfaces
• Phasefield theory for fractional diffusion-reaction equations and applications

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• Some Energy Estimates for Stable Solutions to Fractional Allen-Cahn Equations
• Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface
• Long-range phase coexistence models: recent progress on the fractional Allen-Cahn equation
• Time-fractional Allen-Cahn equations versus powers of the mean curvature
• Stable solutions to the fractional Allen-Cahn equation in the nonlocal perimeter regime