-
1
-
-
31744435328
-
Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
-
M. AGUEH, Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory, Adv. Differential Equations 10 (2005), 309 - 360.
-
(2005)
Adv. Differential Equations
, vol.10
, pp. 309-360
-
-
Agueh, M.1
-
2
-
-
31744443874
-
-
Lectures Math. ETH Zürich, Birkhäuser, Basel
-
L. AMBROSIO, N. GIGLI, and G. SAVARÉ, Gradient flows in metric spaces and in the space of probability measures, Lectures Math. ETH Zürich, Birkhäuser, Basel, 2005.
-
(2005)
Gradient flows in metric spaces and in the space of probability measures
-
-
Ambrosio, L.1
Gigli, N.2
Savaré, G.3
-
3
-
-
79551713648
-
-
Differ. Equ. 3, Elsevier/North-Holland, Amsterdam
-
L. AMBROSIO and G. SAVARÉ, Gradient Flows of Probability Measures, Handb. Differ. Equ. 3, Elsevier/North-Holland, Amsterdam, 2006.
-
(2006)
Gradient Flows of Probability Measures, Handb
-
-
Ambrosio, L.1
Savaré, G.2
-
4
-
-
0031529217
-
A kinetic equation for granular media
-
D. BENEDETTO, E. CAGLIOTI, and M. PULVIRENTI, A kinetic equation for granular media, RAIROModél. Math. Anal. Numér. 31 (1997), 615 - 641.
-
(1997)
RAIROModél. Math. Anal. Numér.
, vol.31
, pp. 615-641
-
-
Benedetto, D.1
Caglioti, E.2
Pulvirenti, M.3
-
5
-
-
77951121715
-
Finite-time blow-up of L∞-weak solutions of an aggregation equation
-
A. L. BERTOZZI and J. BRANDMAN, Finite-time blow-up of L∞-weak solutions of an aggregation equation, Commun. Math. Sci. 8 (2010), 45 - 65.
-
(2010)
Commun. Math. Sci.
, vol.8
, pp. 45-65
-
-
Bertozzi, A.L.1
Brandman, J.2
-
6
-
-
65249090848
-
Blowup in multidimensional aggregation equations with mildly singular interaction kernels
-
A. L. BERTOZZI, J. A. CARRILLO, and T. LAURENT, Blowup in multidimensional aggregation equations with mildly singular interaction kernels, Nonlinearity 22 (2009), 683 - 710.
-
(2009)
Nonlinearity
, vol.22
, pp. 683-710
-
-
Bertozzi, A.L.1
Carrillo, J.A.2
Laurent, T.3
-
7
-
-
34547507325
-
Finite-time blow-up of solutions of an aggregation equation in Rn
-
A. L. BERTOZZI and T. LAURENT, Finite-time blow-up of solutions of an aggregation equation in Rn, Comm. Math. Phys. 274 (2007), 717 - 735.
-
(2007)
Comm. Math. Phys.
, vol.274
, pp. 717-735
-
-
Bertozzi, A.L.1
Laurent, T.2
-
9
-
-
67650727361
-
Blowup of solutions to a diffusive aggregation model
-
P. BILER, G. KARCH, and P. LAURENÇOT, Blowup of solutions to a diffusive aggregation model, Nonlinearity 22 (2009), 1559 - 1568.
-
(2009)
Nonlinearity
, vol.22
, pp. 1559-1568
-
-
Biler, P.1
Karch, G.2
Laurençot, P.3
-
10
-
-
55549135711
-
Convergence of the mass-transport steepest descent scheme for the subcritical Patlak-Keller-Segel model
-
A. BLANCHET, V. CALVEZ, and J. A. CARRILLO, Convergence of the mass-transport steepest descent scheme for the subcritical Patlak-Keller-Segel model, SIAM J. Numer. Anal. 46 (2008), 691 - 721.
-
(2008)
SIAM J. Numer. Anal.
, vol.46
, pp. 691-721
-
-
Blanchet, A.1
Calvez, V.2
Carrillo, J.A.3
-
12
-
-
33645680010
-
Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions
-
A. BLANCHET, J. DOLBEAULT, and B. PERTHAME, Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions, Electron. J. Differential Equations (2006), no. 44.
-
(2006)
Electron. J. Differential Equations
, vol.100
, Issue.44
-
-
Blanchet, A.1
Dolbeault, J.2
Perthame, B.3
-
13
-
-
32644457070
-
An integro-differential equation arising as a limit of individual cell-based models
-
M. BODNAR and J. J. L. VELÁZQUEZ, An integro-differential equation arising as a limit of individual cell-based models, J. Differential Equations 222 (2006), 341 - 380.
-
(2006)
J. Differential Equations
, vol.222
, pp. 341-380
-
-
Bodnar, M.1
Velázquez, J.J.L.2
-
14
-
-
0034148193
-
Modeling the aggregative behavior of ants of the species Polyergus rufescens
-
Nonlinear Anal. Real World Appl
-
S. BOI, V. CAPASSO, and D. MORALE, "Modeling the aggregative behavior of ants of the species Polyergus rufescens" in Spatial Heterogeneity in Ecological Models (Alcalá de Henares, Spain, 1998), Nonlinear Anal. Real World Appl. 1 (2000), 163 - 176.
-
(2000)
Spatial Heterogeneity in Ecological Models (Alcalá de Henares, Spain, 1998)
, vol.1
, pp. 163-176
-
-
Boi, S.1
Capasso, V.2
Morale, D.3
-
15
-
-
33846217387
-
On an aggregation model with long and short range interactions
-
M. BURGER, V. CAPASSO, and D. MORALE, On an aggregation model with long and short range interactions, Nonlinear Anal. Real World Appl. 8 (2007), 939 - 958.
-
(2007)
Nonlinear Anal. Real World Appl.
, vol.8
, pp. 939-958
-
-
Burger, M.1
Capasso, V.2
Morale, D.3
-
16
-
-
57249084869
-
Large time behavior of nonlocal aggregation models with nonlinear diffusion
-
M. BURGER and M. DI FRANCESCO, Large time behavior of nonlocal aggregation models with nonlinear diffusion, Netw. Heterog. Media 3 (2008), 749 - 785.
-
(2008)
Netw. Heterog. Media
, vol.3
, pp. 749-785
-
-
Burger, M.1
Di Francesco, M.2
-
17
-
-
69849111705
-
Double milling in self-propelled swarms from kinetic theory
-
J. A. CARRILLO, M. R. D'ORSOGNA, and V. PANFEROV, Double milling in self-propelled swarms from kinetic theory, Kinet. Relat. Models 2 (2009), 363 - 378.
-
(2009)
Kinet. Relat. Models
, vol.2
, pp. 363-378
-
-
Carrillo, J.A.1
D'Orsogna, M.R.2
Panferov, V.3
-
18
-
-
1542399709
-
Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates
-
J. A. CARRILLO, R. J. MCCANN, and C. VILLANI, Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates, Rev. Mat. Iberoamericana 19 (2003), 971 - 1018.
-
(2003)
Rev. Mat. Iberoamericana
, vol.19
, pp. 971-1018
-
-
Carrillo, J.A.1
Mccann, R.J.2
Villani, C.3
-
19
-
-
32544445429
-
Contractions in the 2-Wasserstein length space and thermalization of granular media
-
J. A. CARRILLO, Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Ration. Mech. Anal. 179 (2006), 217 - 263.
-
(2006)
Arch. Ration. Mech. Anal.
, vol.179
, pp. 217-263
-
-
Carrillo, J.A.1
-
20
-
-
79551711922
-
Uniqueness of bounded solutions to aggregation equations by optimal transport methods
-
Eur. Math. Soc., Zürich
-
J. A. CARRILLO and J. ROSADO, "Uniqueness of bounded solutions to aggregation equations by optimal transport methods" in Proceedings of the 5th European Congress of Mathematicians, Eur. Math. Soc., Zürich, 2010, 3 - 16.
-
(2010)
Proceedings of the 5th European Congress of Mathematicians
, pp. 3-16
-
-
Carrillo, J.A.1
Rosado, J.2
-
21
-
-
36349010169
-
Multi-vehicle flocking: Scalability of cooperative control algorithms using pairwise potentials
-
IEEE, Piscataway, N. J.
-
Y.-L. CHUANG, Y. R. HUANG, M. R. D'ORSOGNA, and A. L. BERTOZZI, "Multi-vehicle flocking: Scalability of cooperative control algorithms using pairwise potentials" in 2007 IEEE International Conference on Robotics and Automation, IEEE, Piscataway, N.J., 2007, 2292 - 2299.
-
(2007)
2007 IEEE International Conference on Robotics and Automation
, pp. 2292-2299
-
-
Chuang, Y.-L.1
Huang, Y.R.2
D'orsogna, M.R.3
Bertozzi, A.L.4
-
22
-
-
0001397844
-
Vlasov equations, Funktsional
-
English translation in Functional Anal. Appl. 13, 115-123
-
R. DOBRUSHIN, Vlasov equations, Funktsional. Anal. i Prilozhen. 13 (1979), 48 - 58; English translation in Functional Anal. Appl. 13 (1979), 115 - 123.
-
(1979)
Anal. i Prilozhen.
, vol.13
, Issue.1979
, pp. 48-58
-
-
Dobrushin, R.1
-
23
-
-
33846704688
-
The Mean-Field Limit for the Dynamics of Large Particle Systems
-
Exp. no. IX, Univ. Nantes, Nantes
-
F. GOLSE, The Mean-Field Limit for the Dynamics of Large Particle Systems, Journées "Équations aux Dérivées Partielles," exp. no. IX, Univ. Nantes, Nantes, 2003.
-
(2003)
Journées "Équations aux Dérivées Partielles,"
-
-
Golse, F.1
-
25
-
-
0032343437
-
The variational formulation of the Fokker-Planck equation
-
R. JORDAN, D. KINDERLEHRER, and F. OTTO, The variational formulation of the Fokker-Planck equation, SIAM J. Math. Anal. 29 (1998), 1 - 17.
-
(1998)
SIAM J. Math. Anal.
, vol.29
, pp. 1-17
-
-
Jordan, R.1
Kinderlehrer, D.2
Otto, F.3
-
26
-
-
0014748565
-
Initiation of slide mold aggregation viewed as an instability
-
E. F. KELLER and L. A. SEGEL, Initiation of slide mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970), 399 - 415.
-
(1970)
J. Theor. Biol.
, vol.26
, pp. 399-415
-
-
Keller, E.F.1
Segel, L.A.2
-
27
-
-
36949038223
-
Local and global existence for an aggregation equation
-
T. LAURENT, Local and global existence for an aggregation equation, Comm. Partial Differential Equations 32 (2007), 1941 - 1964.
-
(2007)
Comm. Partial Differential Equations
, vol.32
, pp. 1941-1964
-
-
Laurent, T.1
-
28
-
-
61649094952
-
n with fractional dissipation
-
n with fractional dissipation, Comm. Math. Phys. 287 (2009), 687 - 703.
-
(2009)
Comm. Math. Phys.
, vol.287
, pp. 687-703
-
-
Li, D.1
Rodrigo, J.2
-
29
-
-
60349124484
-
Refined blowup criteria and nonsymmetric blowup of an aggregation equation
-
D. LI and J. RODRIGO, Refined blowup criteria and nonsymmetric blowup of an aggregation equation, Adv. Math. 220 (2009), 1717 - 1738.
-
(2009)
Adv. Math.
, vol.220
, pp. 1717-1738
-
-
Li, D.1
Rodrigo, J.2
-
30
-
-
77955386860
-
On a nonlocal aggregation model with nonlinear diffusion
-
D. LI and X. ZHANG, On a nonlocal aggregation model with nonlinear diffusion, Discrete Contin. Dyn. Syst. 27 (2010), 301 - 323.
-
(2010)
Discrete Contin. Dyn. Syst.
, vol.27
, pp. 301-323
-
-
Li, D.1
Zhang, X.2
-
31
-
-
3042676199
-
Long-time asymptotics of kinetic models of granular flows
-
H. LI and G. TOSCANI, Long-time asymptotics of kinetic models of granular flows, Arch. Ration. Mech. Anal. 172 (2004), 407 - 428.
-
(2004)
Arch. Ration. Mech. Anal.
, vol.172
, pp. 407-428
-
-
Li, H.1
Toscani, G.2
-
32
-
-
0031161793
-
A convexity principle for interacting gases
-
R. J. MCCANN, A convexity principle for interacting gases, Adv. Math. 128 (1997), 153 - 179.
-
(1997)
Adv. Math.
, vol.128
, pp. 153-179
-
-
Mccann, R.J.1
-
34
-
-
13844298300
-
An interacting particle system modelling aggregation behavior: From individuals to populations
-
D. MORALE, V. CAPASSO, and K. OELSCHLÄGER, An interacting particle system modelling aggregation behavior: From individuals to populations, J. Math. Biol. 50 (2005), 49 - 66.
-
(2005)
J. Math. Biol.
, vol.50
, pp. 49-66
-
-
Morale, D.1
Capasso, V.2
Oelschläger, K.3
-
35
-
-
77955827977
-
The Vlasov equation as a limit of Hamiltonian classical mechanical systems of interacting particles
-
H. NEUNZERT, The Vlasov equation as a limit of Hamiltonian classical mechanical systems of interacting particles, Trans. Fluid Dynamics 18 (1977), 663 - 678.
-
(1977)
Trans. Fluid Dynamics
, vol.18
, pp. 663-678
-
-
Neunzert, H.1
-
36
-
-
1342300494
-
Diffusion and Ecological Problems: Modern Perspectives
-
Springer, Berlin
-
A. OKUBO and S. LEVIN, Diffusion and Ecological Problems: Modern Perspectives, Interdiscip. Appl. Math. 14, Springer, Berlin, 2002.
-
(2002)
Interdiscip. Appl. Math.
, vol.14
-
-
Okubo, A.1
Levin, S.2
-
37
-
-
0001560970
-
The geometry of dissipative evolution equations: The porous medium equation
-
F. OTTO, The geometry of dissipative evolution equations: The porous medium equation, Comm. Partial Differential Equations 26 (2001), 101 - 174.
-
(2001)
Comm. Partial Differential Equations
, vol.26
, pp. 101-174
-
-
Otto, F.1
-
38
-
-
51249193541
-
Random walk with persistence and external bias
-
C. S. PATLAK, Random walk with persistence and external bias, Bull. Math. Biophys. 15 (1953), 311 - 338.
-
(1953)
Bull. Math. Biophys.
, vol.15
, pp. 311-338
-
-
Patlak, C.S.1
-
39
-
-
18144399840
-
Diagonal defect measures, adhesion dynamics and Euler equation
-
F. POUPAUD, Diagonal defect measures, adhesion dynamics and Euler equation, Methods Appl. Anal. 9 (2002), 533 - 561.
-
(2002)
Methods Appl. Anal.
, vol.9
, pp. 533-561
-
-
Poupaud, F.1
-
40
-
-
35949020007
-
Kinetic equations from Hamiltonian dynamics: Markovian limits
-
H. SPOHN, Kinetic equations from Hamiltonian dynamics: Markovian limits, Rev. Modern Phys. 52 (1980), 569 - 615.
-
(1980)
Rev. Modern Phys.
, vol.52
, pp. 569-615
-
-
Spohn, H.1
-
41
-
-
16244371027
-
Swarming patterns in a two-dimensional kinematic model for biological groups
-
C. M. TOPAZ and A. L. BERTOZZI, Swarming patterns in a two-dimensional kinematic model for biological groups, SIAM J. Appl. Math. 65 (2004), 152 - 174.
-
(2004)
SIAM J. Appl. Math.
, vol.65
, pp. 152-174
-
-
Topaz, C.M.1
Bertozzi, A.L.2
-
42
-
-
33748692474
-
A nonlocal continuum model for biological aggregation
-
C. M. TOPAZ, A. L. BERTOZZI, and M. A. LEWIS, A nonlocal continuum model for biological aggregation, Bull. Math. Biol. 68 (2006), 1601 - 1623.
-
(2006)
Bull. Math. Biol.
, vol.68
, pp. 1601-1623
-
-
Topaz, C.M.1
Bertozzi, A.L.2
Lewis, M.A.3
-
43
-
-
0034549474
-
One-dimensional kinetic models of granular flows
-
G. TOSCANI, One-dimensional kinetic models of granular flows, M2AN Math. Model. Nummer. Anal. 34 (2000), 1277 - 1291.
-
(2000)
M2AN Math. Model. Nummer. Anal.
, vol.34
, pp. 1277-1291
-
-
Toscani, G.1
-
44
-
-
2442557820
-
Topics in Optimal Transportation, Grad
-
Providence
-
C. VILLANI, Topics in Optimal Transportation, Grad. Stud. Math., Amer. Math. Soc., Providence, 2003.
-
(2003)
Stud. Math., Amer. Math. Soc.
-
-
Villani, C.1
-
45
-
-
59949100627
-
Optimal Transport, Old and New
-
Springer, Berlin
-
C. VILLANI, Optimal Transport, Old and New, Grundlehren Math. Wiss. 338, Springer, Berlin, 2009.
-
(2009)
Grundlehren Math. Wiss.
, vol.338
-
-
Villani, C.1
|