On Stability in Time of Space Asymptotics of Solutions of Evolution Equations - Cheremnykh, E. V. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We obtain solutions of the heat-conduction equation on a semi-axis that preserve in time the asymptotic representation of the function that determines a solution at initial time. This property is preserved in the presence of a complex-valued power-decreasing potential. We present an estimate for the rate of “destruction” of the structure of a solution.