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A NOTE ON THE AXISYMMETRIC DIFFUSION EQUATION

Part of: Miscellaneous topics - Partial differential equations Partial differential equations Representations of solutions

Published online by Cambridge University Press:  21 July 2021

ALEXANDER E. PATKOWSKI Open the ORCID record for ALEXANDER E. PATKOWSKI [Opens in a new window]
ALEXANDER E. PATKOWSKI*
Affiliation:
1390 Bumps River Road, Centerville, MA02632, USA; e-mail: alexepatkowski@gmail.com
*
e-mail: alexpatk@hotmail.com
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Abstract

We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for $u(r,t)$ as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.

Keywords

axisymmetric diffusion equationBessel functionsMellin transforms

MSC classification

Primary: 35R10: Partial functional-differential equations
Secondary: 35B40: Asymptotic behavior of solutions 35C10: Series solutions
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 3 , July 2021 , pp. 333 - 341
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Copyright
© Australian Mathematical Society 2021

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