Asymptotic Behavior of Solutions to the Diffusion Equation

Abstract

We study asymptotic behavior of solutions to an initial value problem posed for heat equation. For which, we construct an approximate solution to the initial value problem in terms of derivatives of Gaussian by incorporating the moments of initial function. Spatial shifts are introduced into the leading order term as well as penultimate term of the approximation. This paper is continuation to the work of Yanagisawa [14]. 2018, The Indian National Science Academy.