Abstract:
A recently proposed two-dimensional quasi-gasdynamic model of traffic flows is considered. Its Petrovskii parabolicity is analyzed, and the stability of small perturbations against a constant background is investigated. In a nonlinear setting, an energy equality is derived and an energy estimate of the solution is obtained.
Key words:
models of traffic flows, quasi-gasdynamic system of equations, second-order parabolic systems, stability of small perturbations, energy equality.
Citation:
A. A. Zlotnik, “Some properties of the equations governing a two-dimensional quasi-gasdynamic model of traffic flows”, Zh. Vychisl. Mat. Mat. Fiz., 49:2 (2009), 373–381; Comput. Math. Math. Phys., 49:2 (2009), 363–372
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\by A.~A.~Zlotnik
\paper Some properties of the equations governing a~two-dimensional quasi-gasdynamic model of traffic flows
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 2
\pages 373--381
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\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 2
\pages 363--372
\crossref{https://doi.org/10.1134/S0965542509020146}
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Linking options:
https://www.mathnet.ru/eng/zvmmf46
https://www.mathnet.ru/eng/zvmmf/v49/i2/p373
This publication is cited in the following 5 articles:
V. F. Tishkin, M. A. Trapeznikova, A. A. Chechina, N. G. Churbanova, “Modelirovanie transportnykh potokov na osnove kvazigazodinamicheskogo podkhoda i teorii kletochnykh avtomatov s ispolzovaniem superkompyuterov”, Kompyuternye issledovaniya i modelirovanie, 16:1 (2024), 175–194
A. A. Zlotnik, “O postroenii kvazigazodinamicheskikh sistem uravnenii i barotropnoi sistemy s potentsialnoi massovoi siloi”, Matem. modelirovanie, 24:4 (2012), 65–79
A. A. Zlotnik, “On stability of small perturbations for a modified two-dimensional quasi-gasdynamic model of traffic flows”, Math. Models Comput. Simul., 2:6 (2010), 776–781
A. A. Zlotnik, “Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations”, Comput. Math. Math. Phys., 50:2 (2010), 310–321
Citation in format AMSBIB
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