Analysis and numerical methods for nonlocal‐in‐time Allen‐Cahn equation
Analysis and numerical methods for nonlocal‐in‐time Allen‐Cahn equation
Abstract In this paper, we investigate the nonlocal‐in‐time Allen‐Cahn equation (NiTACE), which incorporates a nonlocal operator in time with a finite nonlocal memory. Our objective is to examine the well‐posedness of the NiTACE by establishing the maximal regularity for the nonlocal‐in‐time parabolic equations with fractional power kernels. Furthermore, we derive …