Heat equation on the arithmetic von Koch snowflake
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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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