Probability Theory and Related Fields

, Volume 118, Issue 1, pp 17–36 | Cite as

Heat equation on the arithmetic von Koch snowflake

Article
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Abstract

We investigate the asymptotic behaviour of the heat content as the time t→ 0 for an s-adic von Koch snowflake generated by a square. We show that the heat content satisfies a functional equation which, after appropriate transformations, takes the form of an inhomogeneous renewal equation. We obtain the structure of the solution of this equation in the arithmetic case up to an exponentially small remainder in t.

Key words:

Heat equation Arithmetic Snowflake 

Mathematics Subject Classification (2000)

35K05 60J65 28A80 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  1. 1.School of MathematicsUniversity of BristolBristolUK

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