Asymptotic Radial Solution of Parabolic Tempered Fractional Laplacian Problem

We study parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity by the direct method of moving planes. We first prove several important theorems, such as asymptotic maximum principle, asymptotic narrow region principle and asymptotic strong maximum principle for antisymmetric functions, which are critical factors in the process of moving planes. Then, we further derive some properties of asymptotic radial solution to parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity in a unit ball. These consequences can be applied to investigate more nonlinear nonlocal parabolic equations.