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Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles
Optimal convergence rate of the multitype sticky particle approximation of one-dimensional diagonal hyperbolic systems with monotonic initial data
1. | CERMICS, École des Ponts, UPE, Inria, Champs-sur-Marne, France |
2. | CERMICS, École des Ponts, UPE, Champs-sur-Marne, France |
References:
[1] |
A. M. Andrew, Another efficient algorithm for convex hulls in two dimensions,, Inform. Process. Lett., 9 (1979), 216.
doi: 10.1016/0020-0190(79)90072-3. |
[2] |
S. Bianchini and A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems,, Ann. of Math. (2), 161 (2005), 223.
doi: 10.4007/annals.2005.161.223. |
[3] |
S. Bobkov and M. Ledoux, One dimensional empirical measures, order statistics, and Kantorovich transport distances,, preprint, (). Google Scholar |
[4] |
F. Bouchut, On Zero Pressure Gas Dynamics,, in Series on Advances in Mathematics for Applied Sciences, 22 (1994), 171.
|
[5] |
F. Bouchut and F. James, Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness,, Comm. Partial Differential Equations, 24 (1999), 2173.
doi: 10.1080/03605309908821498. |
[6] |
Y. Brenier and E. Grenier, Sticky particles and scalar conservation laws,, SIAM J. Numer. Anal., 35 (1998), 2317.
doi: 10.1137/S0036142997317353. |
[7] |
A. Bressan and T. Nguyen, Non-existence and non-uniqueness for multidimensional sticky particle systems,, Kinet. Relat. Models, 7 (2014), 205.
doi: 10.3934/krm.2014.7.205. |
[8] |
W. E, Y. G. Rykov and Y. G. Sinai, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics,, Comm. Math. Phys., 177 (1996), 349.
doi: 10.1007/BF02101897. |
[9] |
M. T. Goodrich, Finding the convex hull of a sorted point set in parallel,, Inform. Process. Lett., 26 (1987), 173.
doi: 10.1016/0020-0190(87)90002-0. |
[10] |
R. L. Graham, An efficient algorithm for determining the convex hull of a finite planar set,, Inform. Process. Lett., 1 (1972), 132. Google Scholar |
[11] |
E. Grenier, Existence globale pour le système des gaz sans pression,, C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), 171.
|
[12] |
B. Jourdain, Signed sticky particles and 1D scalar conservation laws,, C. R. Math. Acad. Sci. Paris, 334 (2002), 233.
doi: 10.1016/S1631-073X(02)02251-3. |
[13] |
B. Jourdain and J. Reygner, A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data,, preprint, (). Google Scholar |
[14] |
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts Appl. Math.,, Cambridge University Press, (2002).
doi: 10.1017/CBO9780511791253. |
[15] |
D. Serre, Systems of Conservation Laws I,, Cambridge University Press, (1999).
doi: 10.1017/CBO9780511612374. |
[16] |
M. Vergassola, B. Dubrulle, U. Frisch and A. Noullez, Burgers' equation, devil's staircases and the mass distribution for large-scale structures,, Astron. Astroph., 289 (1994), 325. Google Scholar |
[17] |
C. Villani, Optimal Transport, volume 338 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences],, Springer-Verlag, (2009).
doi: 10.1007/978-3-540-71050-9. |
[18] |
Y. B. Zel'dovitch, Gravitational instability: An approximate theory for large density perturbations,, Astron. Astroph., 5 (1970), 84. Google Scholar |
show all references
References:
[1] |
A. M. Andrew, Another efficient algorithm for convex hulls in two dimensions,, Inform. Process. Lett., 9 (1979), 216.
doi: 10.1016/0020-0190(79)90072-3. |
[2] |
S. Bianchini and A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems,, Ann. of Math. (2), 161 (2005), 223.
doi: 10.4007/annals.2005.161.223. |
[3] |
S. Bobkov and M. Ledoux, One dimensional empirical measures, order statistics, and Kantorovich transport distances,, preprint, (). Google Scholar |
[4] |
F. Bouchut, On Zero Pressure Gas Dynamics,, in Series on Advances in Mathematics for Applied Sciences, 22 (1994), 171.
|
[5] |
F. Bouchut and F. James, Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness,, Comm. Partial Differential Equations, 24 (1999), 2173.
doi: 10.1080/03605309908821498. |
[6] |
Y. Brenier and E. Grenier, Sticky particles and scalar conservation laws,, SIAM J. Numer. Anal., 35 (1998), 2317.
doi: 10.1137/S0036142997317353. |
[7] |
A. Bressan and T. Nguyen, Non-existence and non-uniqueness for multidimensional sticky particle systems,, Kinet. Relat. Models, 7 (2014), 205.
doi: 10.3934/krm.2014.7.205. |
[8] |
W. E, Y. G. Rykov and Y. G. Sinai, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics,, Comm. Math. Phys., 177 (1996), 349.
doi: 10.1007/BF02101897. |
[9] |
M. T. Goodrich, Finding the convex hull of a sorted point set in parallel,, Inform. Process. Lett., 26 (1987), 173.
doi: 10.1016/0020-0190(87)90002-0. |
[10] |
R. L. Graham, An efficient algorithm for determining the convex hull of a finite planar set,, Inform. Process. Lett., 1 (1972), 132. Google Scholar |
[11] |
E. Grenier, Existence globale pour le système des gaz sans pression,, C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), 171.
|
[12] |
B. Jourdain, Signed sticky particles and 1D scalar conservation laws,, C. R. Math. Acad. Sci. Paris, 334 (2002), 233.
doi: 10.1016/S1631-073X(02)02251-3. |
[13] |
B. Jourdain and J. Reygner, A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data,, preprint, (). Google Scholar |
[14] |
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts Appl. Math.,, Cambridge University Press, (2002).
doi: 10.1017/CBO9780511791253. |
[15] |
D. Serre, Systems of Conservation Laws I,, Cambridge University Press, (1999).
doi: 10.1017/CBO9780511612374. |
[16] |
M. Vergassola, B. Dubrulle, U. Frisch and A. Noullez, Burgers' equation, devil's staircases and the mass distribution for large-scale structures,, Astron. Astroph., 289 (1994), 325. Google Scholar |
[17] |
C. Villani, Optimal Transport, volume 338 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences],, Springer-Verlag, (2009).
doi: 10.1007/978-3-540-71050-9. |
[18] |
Y. B. Zel'dovitch, Gravitational instability: An approximate theory for large density perturbations,, Astron. Astroph., 5 (1970), 84. Google Scholar |
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