Effect of decay rates of initial data on the sign of solutions to Cauchy problems of polyharmonic heat equations

Abstract In this paper, we consider the sign of solutions to Cauchy problems linear and semilinear polyharmonic heat equations. for higher order parabolic equations have no positivity preserving property in general, however, it is expected that these are eventually globally positive if initial data decay slowly enough. We first show existence threshold rate datum which separates whether corresponding solution problem equation or not. Applying result, construct under super-Fujita condition.