Error Estimates for Solutions of the Semilinear Parabolic Equation in Whole Space

Abstract

This paper is focused on the error estimates for solutions of the three-dimensional semilinear parabolic equation with initial data $u_0\in L^2({ℝ}^3)$. Employing the energy methods and Fourier analysis technique, it is proved that the error between the solution of the semilinear parabolic equation and that of linear heat equation has the behavior as $O({(1+t)}^{-3/8})$.