메뉴 건너뛰기




Volumn 22, Issue 3, 2009, Pages 683-710

Blow-up in multidimensional aggregation equations with mildly singular interaction kernels

Author keywords

[No Author keywords available]

Indexed keywords


EID: 65249090848     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/3/009     Document Type: Article
Times cited : (215)

References (39)
  • 6
    • 34547507325 scopus 로고    scopus 로고
    • Finite-time blow-up of solutions of an aggregation equation in
    • Bertozzi A L and Laurent T 2007 Finite-time blow-up of solutions of an aggregation equation in Commun. Math. Phys. 274 717-35
    • (2007) Commun. Math. Phys. , vol.274 , Issue.3 , pp. 717-735
    • Bertozzi, A.L.1    Laurent, T.2
  • 7
    • 0345504868 scopus 로고    scopus 로고
    • Global and expoding solutions for nonlocal quadratic evolution problems
    • Biler P and Woyczyński A 1998 Global and expoding solutions for nonlocal quadratic evolution problems SIAM J. Appl. Math. 59 845-69
    • (1998) SIAM J. Appl. Math. , vol.59 , Issue.3 , pp. 845-869
    • Biler, P.1    Woyczyński, A.2
  • 8
    • 52349087894 scopus 로고    scopus 로고
    • Infinite time aggregation for the critical Patlak-Keller-Segel model in
    • Blanchet A, Carrillo J A and Masmoudi N 2008 Infinite time aggregation for the critical Patlak-Keller-Segel model in Commun. Pure Appl. Math. 61 1449-81
    • (2008) Commun. Pure Appl. Math. , vol.61 , Issue.10 , pp. 1449-1481
    • Blanchet, A.1    Carrillo, J.A.2    Masmoudi, N.3
  • 9
    • 33645680010 scopus 로고    scopus 로고
    • Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions
    • Blanchet A, Dolbeault J and Perthame B 2006 Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions J. Diff. Eqns 44 32pp (electronic)
    • (2006) J. Diff. Eqns , vol.44
    • Blanchet, A.1    Dolbeault, J.2    Perthame, B.3
  • 10
    • 32644457070 scopus 로고    scopus 로고
    • An integro-differential equation arising as a limit of individual cell-based models
    • Bodnar M and Velázquez J J L 2006 An integro-differential equation arising as a limit of individual cell-based models J. Diff. Eqns 222 341-80
    • (2006) J. Diff. Eqns , vol.222 , Issue.2 , pp. 341-380
    • Bodnar, M.1    Velázquez, J.J.L.2
  • 11
    • 0034148193 scopus 로고    scopus 로고
    • Modeling the aggregative behavior of ants of the species
    • Boi S, Capasso V and Morale D 2000 Modeling the aggregative behavior of ants of the species Polyergus rufescens Spatial Heterogeneity in Ecological Models (Alcalá de Henares 1998) Nonlinear Anal. Real World Appl. 1 163-76
    • (2000) Nonlinear Anal. Real World Appl. , vol.1 , Issue.1 , pp. 163-176
    • Boi, S.1    Capasso, V.2    Morale, D.3
  • 13
    • 33846217387 scopus 로고    scopus 로고
    • On an aggregation model with long and short range interactions
    • DOI 10.1016/j.nonrwa.2006.04.002, PII S1468121806000514
    • Burger M, Capasso V and Morale D 2007 On an aggregation model with long and short range interactions Nonlinear Anal. Real World Appl. 8 939-58 (Pubitemid 46097518)
    • (2007) Nonlinear Analysis: Real World Applications , vol.8 , Issue.3 , pp. 939-958
    • Burger, M.1    Capasso, V.2    Morale, D.3
  • 14
    • 65249148574 scopus 로고    scopus 로고
    • Large time behavior of nonlocal aggregation models with nonlinear diffusion
    • Burger M and Di Francesco M 2009 Large time behavior of nonlocal aggregation models with nonlinear diffusion Netw. Heterogenous Media at press
    • (2009) Netw. Heterogenous Media
    • Burger, M.1    Di Francesco, M.2
  • 15
    • 1542399709 scopus 로고    scopus 로고
    • Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates
    • Carrillo J A, McCann R J and Villani C 2003 Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates Rev. Mat. Iberoamericana 19 1-48 (Pubitemid 38355024)
    • (2003) Revista Matematica Iberoamericana , vol.19 , Issue.3 , pp. 971-1018
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 16
    • 32544445429 scopus 로고    scopus 로고
    • Contractions in the 2-Wasserstein length space and thermalization of granular media
    • Carrillo J A, McCann R J and Villani C 2006 Contractions in the 2-Wasserstein length space and thermalization of granular media Arch. Ration. Mech. Anal. 179 217-63
    • (2006) Arch. Ration. Mech. Anal. , vol.179 , Issue.2 , pp. 217-263
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 18
    • 18644382851 scopus 로고    scopus 로고
    • Optimal critical mass in the two-dimensional Keller-Segel model in
    • Dolbeault J and Perthame B 2004 Optimal critical mass in the two-dimensional Keller-Segel model in C. R. Math. Acad. Sci. Paris 339 611-16
    • (2004) C. R. Math. Acad. Sci. Paris , vol.339 , Issue.9 , pp. 611-616
    • Dolbeault, J.1    Perthame, B.2
  • 20
    • 33747055534 scopus 로고    scopus 로고
    • Formation of clumps and patches in self-aggregation of finite-size particles
    • DOI 10.1016/j.physd.2006.07.010, PII S0167278906002387
    • Holm D and Putkaradze V 2006 Formation of clumps and patches in self-aggregation of finite-size particles Physica D 220 183-96 (Pubitemid 44216019)
    • (2006) Physica D: Nonlinear Phenomena , vol.220 , Issue.2 , pp. 183-196
    • Holm, D.D.1    Putkaradze, V.2
  • 21
    • 28844432303 scopus 로고    scopus 로고
    • Aggregation of finite size particles with variable mobility
    • Holm D and Putkaradze V 2005 Aggregation of finite size particles with variable mobility Phys. Rev. Lett. 95 226106
    • (2005) Phys. Rev. Lett. , vol.95 , Issue.22 , pp. 226106
    • Holm, D.1    Putkaradze, V.2
  • 22
    • 0014748565 scopus 로고
    • Initiation of slide mold aggregation viewed as an instability
    • Keller E F and Segel L A 1970 Initiation of slide mold aggregation viewed as an instability J. Theor. Biol. 26 399-415
    • (1970) J. Theor. Biol. , vol.26 , Issue.3 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 23
    • 36949038223 scopus 로고    scopus 로고
    • Local and global existence for an aggregation equation
    • Laurent T 2007 Local and global existence for an aggregation equation Commun. Partial Diff. Eqns 32 1941-64
    • (2007) Commun. Partial Diff. Eqns , vol.32 , Issue.12 , pp. 1941-1964
    • Laurent, T.1
  • 24
    • 65249175157 scopus 로고    scopus 로고
    • Finite-time singularities of an aggregation equation in with fractional dissipation
    • Li D and Rodrigo J 2008 Finite-time singularities of an aggregation equation in with fractional dissipation Commun. Math. Phys. at press
    • (2008) Commun. Math. Phys.
    • Li, D.1    Rodrigo, J.2
  • 25
    • 65249147229 scopus 로고    scopus 로고
    • Refined blowup criteria and nonsymmetric blowup of an aggregation equation
    • Li D and Rodrigo J 2008 Refined blowup criteria and nonsymmetric blowup of an aggregation equation Adv. Math. at press
    • (2008) Adv. Math.
    • Li, D.1    Rodrigo, J.2
  • 27
    • 3042676199 scopus 로고    scopus 로고
    • Long-time asymptotics of kinetic models of granular flows
    • DOI 10.1007/s00205-004-0307-8
    • Li H and Toscani G 2004 Long-time asymptotics of kinetic models of granular flows Arch. Ration. Mech. Anal. 172 407-28 (Pubitemid 38808952)
    • (2004) Archive for Rational Mechanics and Analysis , vol.172 , Issue.3 , pp. 407-428
    • Li, H.1    Toscani, G.2
  • 29
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • DOI 10.1006/aima.1997.1634, PII S0001870897916340
    • McCann R J 1997 A convexity principle for interacting gases Adv. Math. 128 153-79 (Pubitemid 127171227)
    • (1997) Advances in Mathematics , vol.128 , Issue.1 , pp. 153-179
    • McCann, R.J.1
  • 31
    • 13844298300 scopus 로고    scopus 로고
    • An interacting particle system modelling aggregation behavior: From individuals to populations
    • DOI 10.1007/s00285-004-0279-1
    • Morale D, Capasso V and Oelschläger K 2005 An interacting particle system modelling aggregation behavior: from individuals to populations J. Math. Biol. 50 49-66 (Pubitemid 40240753)
    • (2005) Journal of Mathematical Biology , vol.50 , Issue.1 , pp. 49-66
    • Morale, D.1    Capasso, V.2    Oelschlager, K.3
  • 33
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • Otto F 2001 The geometry of dissipative evolution equations: the porous medium equation Commun. Partial Diff. Eqns 26 101-74 (Pubitemid 33731270)
    • (2001) Communications in Partial Differential Equations , vol.26 , Issue.1-2 , pp. 101-174
    • Otto, F.1
  • 34
    • 51249193541 scopus 로고
    • Random walk with persistence and external bias
    • Patlak C S 1953 Random walk with persistence and external bias Bull. Math. Biophys. 15 311-8
    • (1953) Bull. Math. Biophys. , vol.15 , Issue.3 , pp. 311-318
    • Patlak, C.S.1
  • 35
    • 16244371027 scopus 로고    scopus 로고
    • Swarming patterns in a two-dimensional kinematic model for biological groups
    • Topaz C M and Bertozzi A L 2004 Swarming patterns in a two-dimensional kinematic model for biological groups SIAM J. Appl. Math. 65 152-74
    • (2004) SIAM J. Appl. Math. , vol.65 , Issue.1 , pp. 152-174
    • Topaz, C.M.1    Bertozzi, A.L.2
  • 36
    • 33748692474 scopus 로고    scopus 로고
    • A nonlocal continuum model for biological aggregation
    • DOI 10.1007/s11538-006-9088-6
    • Topaz C M, Bertozzi A L and Lewis M A 2006 A nonlocal continuum model for biological aggregation Bull. Math. Biol. 68 1601-23 (Pubitemid 44392962)
    • (2006) Bulletin of Mathematical Biology , vol.68 , Issue.7 , pp. 1601-1623
    • Topaz, C.M.1    Bertozzi, A.L.2    Lewis, M.A.3
  • 37
    • 0034549474 scopus 로고    scopus 로고
    • One-dimensional kinetic models of granular flows
    • DOI 10.1051/m2an:2000127
    • Toscani G 2000 One-dimensional kinetic models of granular flows RAIRO Modélling Math. Anal. Numér. 34 1277-91 (Pubitemid 33220541)
    • (2000) Mathematical Modelling and Numerical Analysis , vol.34 , Issue.6 , pp. 1277-1291
    • Toscani, G.1
  • 39
    • 0001751564 scopus 로고
    • Non-stationary flow of an incompressible liquid
    • Yudovich V I 1963 Non-stationary flow of an incompressible liquid Zh. Vychisl. Mat. Mat. Fiz. 3 1032-66
    • (1963) Zh. Vychisl. Mat. Mat. Fiz. , vol.3 , pp. 1032-1066
    • Yudovich, V.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.