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Archive for rational mechanics and analysis, ISSN 1432-0673, 2019, Volume 233, Issue 3, pp. 1289 - 1317
A new type of differential equations for probability measures on Euclidean spaces, called measure differential equations (briefly MDEs), is introduced. MDEs... 
MATHEMATICS, APPLIED | MECHANICS | Differential equations | Diffusion rate | Euclidean geometry | Convolution | Partial differential equations | Mathematical analysis | Dependence | Ordinary differential equations | Mapping | Euclidean space | Fields (mathematics) | Monoids
Journal Article
2003, Volume 12, 2
Reference
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 3/2011, Volume 199, Issue 3, pp. 707 - 738
... edestrian Flow Benedetto Piccoli & Andrea Tosin Communicated by C. M. Dafermos Abstract This paper introduces a new model of pedestrian flow, formulated within a measure... 
Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | TRAFFIC FLOW | DYNAMICS | WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS
Journal Article
Archive for rational mechanics and analysis, ISSN 1432-0673, 2013, Volume 211, Issue 1, pp. 335 - 358
... to Transport Equations with Source Benedetto Piccoli & Francesco Rossi Communicated by C. Dafermos Abstract In this article, we generalize the Wasserstein distance... 
Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SPACES | FLOW | Archives
Journal Article
Archive for rational mechanics and analysis, ISSN 1432-0673, 2016, Volume 222, Issue 3, pp. 1339 - 1365
Journal Article
Multiscale modeling & simulation, ISSN 1540-3467, 2011, Volume 9, Issue 1, pp. 155 - 182
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 03/2015, Volume 25, Issue 3, pp. 521 - 564
Journal Article
2004, Mathématiques & applications, ISBN 3540203060, Volume 43, xiii, 261
Book
Communications in Mathematical Sciences, ISSN 1539-6746, 2016, Volume 14, Issue 3, pp. 683 - 704
Journal Article
Acta Applicandae Mathematicae, ISSN 0167-8019, 4/2013, Volume 124, Issue 1, pp. 73 - 105
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 06/2017, Volume 27, Issue 7, pp. 1223 - 1253
We consider nonlinear transport equations with non-local velocity describing the time-evolution of a measure. Such equations often appear when considering the... 
crowd control | control systems | networked control | distributed parameter systems | control of partial differential equations | Lyapunov methods | Multi-agent systems | MATHEMATICS, APPLIED | STABILIZATION | CONSENSUS | MODEL | DYNAMICS | TRANSPORT-EQUATION | CONTROLLABILITY | FLOCKING
Journal Article
Continuum Mechanics and Thermodynamics, ISSN 0935-1175, 07/2009, Volume 21, Issue 2, pp. 85 - 107
In this paper, we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of... 
Pedestrian flow | Measure theory | Push forward | Macroscopic modeling | WAVES | MECHANICS | THERMODYNAMICS | MODELS | TRAFFIC FLOW | CROWD DYNAMICS | Pedestrians | Analysis | Mathematical models | Group dynamics
Journal Article
SIAM JOURNAL ON APPLIED MATHEMATICS, ISSN 0036-1399, 2019, Volume 79, Issue 2, pp. 641 - 667
We consider a strongly coupled ODE-PDE system representing moving bottlenecks immersed in vehicular traffic. The systems can be used to represent the effect of... 
backwards in time method | ODE | SHOCK | MATHEMATICS, APPLIED | WAVES | BOTTLENECKS | TRAFFIC FLOW | traffic flow modeling | tangent vectors | wavefront tracking | scalar conservation laws with constraints
Journal Article
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 11/2014, Volume 372, Issue 2028, p. 20130400
Journal Article
Transportmetrica. (Abingdon, Oxfordshire, UK), ISSN 2168-0582, 2015, Volume 4, Issue 3, pp. 187 - 222
Journal Article
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