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Heat equation on the arithmetic von Koch snowflake
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  • Published: 12 February 2014

Heat equation on the arithmetic von Koch snowflake

  • M. van den Berg1 

Probability Theory and Related Fields volume 118, pages 17–36 (2000)Cite this 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. <!-ID=""Mathematics Subject Classification (2000): 35K05, 60J65, 28A80--> <!-ID=""Key words: Heat equation – Arithmetic – Snowflake-->

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Authors and Affiliations

  1. School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom. e-mail: M.vandenBerg@bris.ac.uk, UK

    M. van den Berg

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  1. M. van den Berg
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Received: 24 March 1999 / Revised version: 14 October 1999 / Published online : 8 August 2000

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van den Berg, M. Heat equation on the arithmetic von Koch snowflake. Probab Theory Relat Fields 118, 17–36 (2000). https://doi.org/10.1007/PL00008740

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  • Published: 12 February 2014

  • Issue Date: September 2000

  • DOI: https://doi.org/10.1007/PL00008740

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Keywords

  • Heat Content
  • Brownian Motion
  • Heat Equation
  • Fractal Boundary
  • Half Line
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