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
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Abstract
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.
References
|
[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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