Formula for the fundamental solution of the heat equation on the sphere

✍ Scribed by V. Tulovsky; L. Papiez

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 192 KB
• Volume: 14
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(01)00059-3

✦ Synopsis

This paper is devoted to the derivation of a simple asymptotic formula for the fundamental solution of the heat equation on the sphere. This formula is efficient for small values of the evolution parameter, and thus, complements the well-known formula for the fundamental solution in terms of Legendre polynomials that is efficient for relatively large values of the evolution parameter. The method relies on constructing a self-similar solution. (~) 2001 Elsevier Science Ltd. All rights reserved.