Choi, ByoungSeon Kim, Chansoo Kang, Hyuk Choi, M. Y. 2024-01-19T18:03:53Z 2024-01-19T18:03:53Z 2021-09-04 2020-02 0378-4371 https://pubs.kist.re.kr/handle/201004/118979 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. (C) 2019 Elsevier B.V. All rights reserved. English Elsevier BV General solutions of the heat equation Article 10.1016/j.physa.2019.122914 1 Physica A: Statistical Mechanics and its Applications, v.539 Physica A: Statistical Mechanics and its Applications 539 N scie scopus 000503317700008 2-s2.0-85073098207 Physics, Multidisciplinary Physics Article BROWNIAN DIFFUSION MAXIMUM Heat equation Diffusion equation Boundary-value problem Hermite polynomials