Mathematical Biosciences and Engineering

2015, Issue 2: 279-290. doi: 10.3934/mbe.2015.12.279

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

• Received: 01 April 2014 Accepted: 29 June 2018 Published: 01 December 2014
• MSC : Primary: 00A71, 35L65; Secondary: 92D25.

• In this note we explain by an example what we understandby a balance situation and by a balance equation in termsof measures.
The latter ones are an attempt to start modelling of (not only)diffusion-reaction or mass-conservation scenarios in terms of measuresrather 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 andphysical motion in populations or physical motion and formation of polymers by means of a single model equation.

Citation: Michael Böhm, Martin Höpker. A note on modelling with measures: Two-features balance equations[J]. Mathematical Biosciences and Engineering, 2015, 12(2): 279-290. doi: 10.3934/mbe.2015.12.279

Related Papers:

• In this note we explain by an example what we understandby a balance situation and by a balance equation in termsof measures.
The latter ones are an attempt to start modelling of (not only)diffusion-reaction or mass-conservation scenarios in terms of measuresrather 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 andphysical motion in populations or physical motion and formation of polymers by means of a single model equation.
 [1] BirkhäuserBoston, Inc., Boston, MA, 1998. [2] Lecture Notes, in preparation. [3] Springer, 1974. [4] Journal of Contaminant Hydrology, 1 (1987), 309-327. [5] XIX International Conference on Water Resources, CMWR, 2012. [6] Continuum Mech. Thermodyn., 13 (2001), 149-169. [7] Collective Dynamics from Bacteria to Crowds, CISM International Centre for Mechanical Sciences, 553 (2014), 75-103. [8] Arch. Ration. Mech. Anal., 1984 (2007), 169-196. [9] Arch. Rational Mech. Anal., 154 (2000), 183-198. [10] Springer, Berlin, 1997. [11] Pure and Applied Chemistry, 83 (2011), 2229-2259. [12] $2^{nd}$ edition, Cambridge University Press, 2001. [13] $1^{st}$ edition, AcademicPress, Boston, 1991.

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