Generalized Wasserstein distance and its application to transport equations with source

@inproceedings{Piccoli2013GeneralizedWD,
  title={Generalized Wasserstein distance and its application to transport equations with source},
  author={Benedetto Piccoli and Francesco Rossi},
  year={2013}
}
In this article, we generalize the Wasserstein distance to measures with di erent masses. We study the properties of such distance. In particular, we show that it metrizes weak convergence for tight sequences. We use this generalized Wasserstein distance to study a transport equation with source, in which both the vector eld and the source depend on the measure itself. We prove existence and uniqueness of the solution to the Cauchy problem when the vector eld and the source are Lipschitzian… CONTINUE READING
Highly Cited
This paper has 38 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 26 extracted citations

Sparse Dynamic Filtering via Earth Mover's Distance Regularization

2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) • 2018
View 1 Excerpt

References

Publications referenced by this paper.
Showing 1-10 of 24 references

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes, Acta Applicandae Mathematicae, 124, pp

B. Piccoli, F. Rossi
73 105, • 2013
View 6 Excerpts
Highly Influenced

R

L. C. Evans
F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, • 1992
View 4 Excerpts
Highly Influenced

Topics in Optimal Transportation, Graduate Studies in Mathematics, Vol

C. Villani
58, • 2003
View 6 Excerpts
Highly Influenced

Transport equation with nonlocal velocity in Wasserstein spaces : convergence of numerical schemes

F. Rossi B. Piccoli
Acta Applicandae Mathematicae • 2013

Modeling Micro-Macro Pedestrian Counter ow in Heterogeneous Domains, Nonlinear Phenomena in Complex Systems, Volume 14, Number 1, pp

J. Evers, A. Muntean
27 37, • 2011
View 1 Excerpt

Similar Papers

Loading similar papers…