General solutions of the heat equation

ByoungSeon Choi, Chansoo Kim, Hyuk Kang and M.Y. Choi

Physica A: Statistical Mechanics and its Applications, 2020, vol. 539, issue C

Abstract: We derive a general solution of the heat equation through the use of the similarity reduction method. The obtained solution is expressed as linearly combined kernel solutions in terms of the Hermite polynomials, which appears to provide an explanation of non-Gaussian behavior observed in various cases. As examples, we consider a few typical boundary conditions and construct corresponding solutions, demonstrating the versatile applicability of our scheme. It is thus revealed that the heat equation carries many solutions under given boundary conditions. The entropy borne by a non-Gaussian solution is also computed and shown to approach in the long-time limit the maximum one corresponding to the fundamental (Gaussian) solution.

Keywords: Heat equation; Diffusion equation; Boundary-value problem; Hermite polynomials (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843711931653X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:539:y:2020:i:c:s037843711931653x

DOI: 10.1016/j.physa.2019.122914

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().