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.
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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/s004400000068
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DOI: https://doi.org/10.1007/s004400000068
Mathematics Subject Classification (2000)
- 35K05
- 60J65
- 28A80
Key words:
- Heat equation
- Arithmetic
- Snowflake