Indian Journal of Pure and Applied Mathematics

, Volume 49, Issue 4, pp 601–620 | Cite as

Asymptotic Behavior of Solutions to the Diffusion Equation

  • Satyanarayana EnguEmail author
  • Ahmed Mohd
  • Manas Ranjan Sahoo


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].

Key words

Asymptotic behavior Cole-Hopf transformation heat equation 


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Copyright information

© The Indian National Science Academy 2018

Authors and Affiliations

  • Satyanarayana Engu
    • 1
    Email author
  • Ahmed Mohd
    • 1
  • Manas Ranjan Sahoo
    • 2
    • 3
  1. 1.Department of Mathematical and Computational SciencesNational Institute of Technology KarnatakaSurathkalIndia
  2. 2.School of Mathematical SciencesNational Institute of Science Education and ResearchBhubaneswarIndia
  3. 3.Homi Bhaba National Institute (HBNI), Training School Complex, Anushakti NagarMumbaiIndia

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