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Conditionally integrable nonlinear diffusion with diffusivity 1/u

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posted on 2021-01-14, 05:22 authored by Philip BroadbridgePhilip Broadbridge, Joanna M Goard
© 2019 by the authors.

An explicit mapping is given from the space of general complex meromorphic functions to a space of special time-dependent solutions of the 1 + 2-dimensional nonlinear diffusion equation with diffusivity depending on concentration as D=1/u. These solutions have constant-flux boundary conditions. Some simple examples are constructed, including that of a line source enclosed by a cylindrical barrier. This has direct application to electron diffusion in a laser-heated plasma.

Funding

The first author is grateful for the support of the Australian Research Council through Project DP160101366.

History

Publication Date

2019-01-01

Journal

Symmetry

Volume

11

Issue

6

Article Number

804

Pagination

10p.

Publisher

MDPI AG

ISSN

2073-8994

Rights Statement

The Author reserves all moral rights over the deposited text and must be credited if any re-use occurs. Documents deposited in OPAL are the Open Access versions of outputs published elsewhere. Changes resulting from the publishing process may therefore not be reflected in this document. The final published version may be obtained via the publisher’s DOI. Please note that additional copyright and access restrictions may apply to the published version.

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