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A note on modelling with measures: Two-features balance equations
1. | Center for Industrial Mathematics, University of Bremen, Bibliothekstrasse 1, D-28359 Bremen, Germany, Germany |
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.
References:
[1] |
V. Agoshkov, Boundary Value Problems for Transport Equations, BirkhäuserBoston, Inc., Boston, MA, 1998.
doi: 10.1007/978-1-4612-1994-1. |
[2] | |
[3] | |
[4] |
P. M. Gschwend and M. D. Reynolds, Monodisperse ferrous phosphate colloids in an anoxic groundwater plume, Journal of Contaminant Hydrology, 1 (1987), 309-327.
doi: 10.1016/0169-7722(87)90011-8. |
[5] |
O. Krehel, A. Muntean and P. Knabner, On Modeling and Simulation of Flocculation in Porous Media, XIX International Conference on Water Resources, CMWR, 2012. |
[6] |
A. Marzocchi and A. Musesti, Decomposition and integral representation of Cauchy interactions associated with measures, Continuum Mech. Thermodyn., 13 (2001), 149-169.
doi: 10.1007/s001610100046. |
[7] |
A. Muntean, E. N. M. Cirillo, O. Krehel and M. Böhm, Pedestrians moving in the dark: Balancing measures and playing games on lattices, Collective Dynamics from Bacteria to Crowds, CISM International Centre for Mechanical Sciences, 553 (2014), 75-103.
doi: 10.1007/978-3-7091-1785-9_3. |
[8] |
F. Schuricht, A new mathematical foundation for contact interactions in continuum physics, Arch. Ration. Mech. Anal., 1984 (2007), 169-196. |
[9] |
R. Segev, The geometry of Cauchy fluxes, Arch. Rational Mech. Anal., 154 (2000), 183-198.
doi: 10.1007/s002050000089. |
[10] |
M. Šilhavý, The Mechanics and Thermodynamics of Continuous Media, Springer, Berlin, 1997.
doi: 10.1007/978-3-662-03389-0. |
[11] |
S. Slomkowski, J. Alemán, R. G. Gilbert, M. Hess, K. Horie, R. G. Jones, P. Kubisa, I. Meisel, W. Mormann, S. Penczek and R. F. T. Stepto, Terminology of polymers and polymerization processes in dispersed systems (IUPAC Recommendations 2011), Pure and Applied Chemistry, 83 (2011), 2229-2259.
doi: 10.1351/PAC-REC-10-06-03. |
[12] |
R. Temam and A. Miranville, Mathematical Modeling in Continuum Mechanics, $2^{nd}$ edition, Cambridge University Press, 2001. |
[13] |
C. Truesdell, A First Course in Rational Continuum Mechanics, $1^{st}$ edition, AcademicPress, Boston, 1991. |
show all references
References:
[1] |
V. Agoshkov, Boundary Value Problems for Transport Equations, BirkhäuserBoston, Inc., Boston, MA, 1998.
doi: 10.1007/978-1-4612-1994-1. |
[2] | |
[3] | |
[4] |
P. M. Gschwend and M. D. Reynolds, Monodisperse ferrous phosphate colloids in an anoxic groundwater plume, Journal of Contaminant Hydrology, 1 (1987), 309-327.
doi: 10.1016/0169-7722(87)90011-8. |
[5] |
O. Krehel, A. Muntean and P. Knabner, On Modeling and Simulation of Flocculation in Porous Media, XIX International Conference on Water Resources, CMWR, 2012. |
[6] |
A. Marzocchi and A. Musesti, Decomposition and integral representation of Cauchy interactions associated with measures, Continuum Mech. Thermodyn., 13 (2001), 149-169.
doi: 10.1007/s001610100046. |
[7] |
A. Muntean, E. N. M. Cirillo, O. Krehel and M. Böhm, Pedestrians moving in the dark: Balancing measures and playing games on lattices, Collective Dynamics from Bacteria to Crowds, CISM International Centre for Mechanical Sciences, 553 (2014), 75-103.
doi: 10.1007/978-3-7091-1785-9_3. |
[8] |
F. Schuricht, A new mathematical foundation for contact interactions in continuum physics, Arch. Ration. Mech. Anal., 1984 (2007), 169-196. |
[9] |
R. Segev, The geometry of Cauchy fluxes, Arch. Rational Mech. Anal., 154 (2000), 183-198.
doi: 10.1007/s002050000089. |
[10] |
M. Šilhavý, The Mechanics and Thermodynamics of Continuous Media, Springer, Berlin, 1997.
doi: 10.1007/978-3-662-03389-0. |
[11] |
S. Slomkowski, J. Alemán, R. G. Gilbert, M. Hess, K. Horie, R. G. Jones, P. Kubisa, I. Meisel, W. Mormann, S. Penczek and R. F. T. Stepto, Terminology of polymers and polymerization processes in dispersed systems (IUPAC Recommendations 2011), Pure and Applied Chemistry, 83 (2011), 2229-2259.
doi: 10.1351/PAC-REC-10-06-03. |
[12] |
R. Temam and A. Miranville, Mathematical Modeling in Continuum Mechanics, $2^{nd}$ edition, Cambridge University Press, 2001. |
[13] |
C. Truesdell, A First Course in Rational Continuum Mechanics, $1^{st}$ edition, AcademicPress, Boston, 1991. |
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