A note on modelling with measures: Two-features balance equations

Michael Böhm; Martin Höpker

doi:10.3934/mbe.2015.12.279

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2015, Volume 12, Issue 2: 279-290. Doi: 10.3934/mbe.2015.12.279 open access

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A note on modelling with measures: Two-features balance equations

Michael Böhm^1, and
Martin Höpker^1,

1.
Center for Industrial Mathematics, University of Bremen, Bibliothekstrasse 1, D-28359 Bremen

Received: March 31, 2014

Revised: September 30, 2014

Published: November 2014

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Abstract

In this note we explain by an example what we understand by a balance situation and by a balance equation in terms of measures.
The latter ones are an attempt to start modelling of (not only) diffusion-reaction or mass-conservation scenarios in terms of measures rather than by derivatives and other rates.
By means of three examples this concept is extended to two-features (= two-traits-) balance situations, which, e.g., combine features like aging and physical motion in populations or physical motion and formation of polymers by means of a single model equation.

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Mathematics Subject Classification: Primary: 00A71, 35L65; Secondary: 92D25.

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