La Trobe

File(s) under permanent embargo

Reason: Copyright restrictions by publisher

On transport through heterogeneous media: application of conjugated reciprocal transformations

journal contribution
posted on 2021-03-31, 05:34 authored by C Rogers, Philip BroadbridgePhilip Broadbridge
© 2020, Springer Nature Switzerland AG. Conjugation of reciprocal transformations is used to solve a class of boundary value problems involving a source term relevant to water transport through a heterogeneous medium with a volumetric extraction mechanism. The main emphasis is the solution method that involves conjugation of reciprocal transformations, as well as other changes of variable, applied to a newly identified integrable model. The transport equation is a version of the nonlinear Richards equation, based on Buckingham’s extension of Darcy’s law to unsaturated media, now allowing for heterogeneous transport coefficients. In addition, there is a plant-root water extraction term that depends on both water content and position. The nonlinear boundary conditions have prescribed flux at one boundary and zero flux at the other barrier boundary of a one-dimensional heterogeneous medium.


Publication Date



Zeitschrift fuer Angewandte Mathematik und Physik





Article Number





Springer Nature



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.