Asymptotic Property of Parabolic Equations Involving Pseudo-relativistic Schrödinger Operators

In this paper, we investigate parabolic equations involving nonlocal pseudo-relativistic Schrödinger operators (−Δ + m²)^s with s ∈ (0, 1) and mass m > 0 in bounded regions. We establish the asymptotic narrow region principle and asymptotic strong maximum principle for anti symmetric function. As applications, employing the method of moving planes, we show the asymptotical radial symmetry and monotonicity of positive solutions in an unit ball.