Symmetry of Ancient Solution for Fractional Parabolic Equation Involving Logarithmic Laplacian

Abstract

In this research, we focus on the symmetry of an ancient solution for a fractional parabolic equation involving logarithmic Laplacian in an entire space. In the process of studying the property of a fractional parabolic equation, we obtained some maximum principles, such as the maximum principle of anti-symmetric function, narrow region principle, and so on. We will demonstrate how to apply these tools to obtain radial symmetry of an ancient solution.

Keywords

• ancient solution
• logarithmic Laplacian
• sub-solution