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We study the evolution of a non-relativistically expanding thin shell inradio-emitting tidal disruption events (TDEs) based on a one-dimensionalspherically symmetric model considering the effect of both a time-dependentmass loss rate of the disk wind and the ambient mass distribution. Theanalytical solutions are derived in two extreme limits: one is the approximatesolution near the origin in the form of the Taylor series, and the other is theasymptotic solution in which the ambient matter is dominant far away from theorigin. Our numerical solutions are confirmed to agree with the respectiveanalytical solutions. We find that no simple power-law of time solution existsin early to middle times because the mass loss rate varies over time, affectingthe shell dynamics. We also discuss the application of our model to theobserved radio-emitting TDE, AT2019dsg.

Disk-wind-driven Expanding Radio-emitting Shell in Tidal Disruption Events