Abstract
In this paper, we investigate the existence, uniqueness, and asymptotic behaviors of mild solutions of parabolic evolution equations on complex plane, in which the diffusion operator has the form [Formula: see text], where [Formula: see text], the function [Formula: see text] is smooth and subharmonic on [Formula: see text], and [Formula: see text] is the formal adjoint of [Formula: see text]. Our method combines certain estimates of heat kernel associating with the homogeneous linear equation of Raich [Heat equations in [Formula: see text], J. Funct. Anal. 240(1) (2006) 1–35] and a fixed point argument.
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