메뉴 건너뛰기




Volumn 258, Issue 4, 2010, Pages 1273-1309

Nonlinear mobility continuity equations and generalized displacement convexity

Author keywords

Displacement convexity; Gradient flows; Nonlinear diffusion equations; Nonlinear mobility; Parabolic equations; Wasserstein distance

Indexed keywords


EID: 70450225042     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2009.10.016     Document Type: Article
Times cited : (97)

References (43)
  • 1
    • 2442517322 scopus 로고    scopus 로고
    • Geometric inequalities via a general comparison principle for interacting gases
    • Agueh M., Ghoussoub N., and Kang X. Geometric inequalities via a general comparison principle for interacting gases. Geom. Funct. Anal. 14 14 (2004) 215-244
    • (2004) Geom. Funct. Anal. , vol.14 , Issue.14 , pp. 215-244
    • Agueh, M.1    Ghoussoub, N.2    Kang, X.3
  • 2
    • 33746157912 scopus 로고    scopus 로고
    • Gradient Flows in Metric Spaces and in the Space of Probability Measures
    • Birkhäuser Verlag, Basel
    • Ambrosio L., Gigli N., and Savaré G. Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures Math. ETH Zürich (2005), Birkhäuser Verlag, Basel
    • (2005) Lectures Math. ETH Zürich
    • Ambrosio, L.1    Gigli, N.2    Savaré, G.3
  • 4
    • 84966220156 scopus 로고
    • A generalized Poincaré inequality for Gaussian measures
    • Beckner W. A generalized Poincaré inequality for Gaussian measures. Proc. Amer. Math. Soc. 105 (1989) 397-400
    • (1989) Proc. Amer. Math. Soc. , vol.105 , pp. 397-400
    • Beckner, W.1
  • 5
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • Benamou J.-D., and Brenier Y. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375-393
    • (2000) Numer. Math. , vol.84 , pp. 375-393
    • Benamou, J.-D.1    Brenier, Y.2
  • 6
    • 0000019424 scopus 로고    scopus 로고
    • The mathematics of moving contact lines in thin liquid films
    • Bertozzi A. The mathematics of moving contact lines in thin liquid films. Notices Amer. Math. Soc. 45 (1998) 689-697
    • (1998) Notices Amer. Math. Soc. , vol.45 , pp. 689-697
    • Bertozzi, A.1
  • 7
    • 14644430136 scopus 로고    scopus 로고
    • Extended Monge-Kantorovich theory
    • Optimal Transportation and Applications. Martina Franca, 2001, Springer, Berlin
    • Brenier Y. Extended Monge-Kantorovich theory. Optimal Transportation and Applications. Martina Franca, 2001. Lecture Notes in Math. vol. 1813 (2003), Springer, Berlin 91-121
    • (2003) Lecture Notes in Math. , vol.1813 , pp. 91-121
    • Brenier, Y.1
  • 8
    • 34248370060 scopus 로고    scopus 로고
    • The Keller-Segel model for chemotaxis with prevention of overcrowding: Linear vs. nonlinear diffusion
    • Burger M., di Francesco M., and Dolak Y. The Keller-Segel model for chemotaxis with prevention of overcrowding: Linear vs. nonlinear diffusion. SIAM J. Math. Anal. 38 (2006) 1288-1315
    • (2006) SIAM J. Math. Anal. , vol.38 , pp. 1288-1315
    • Burger, M.1    di Francesco, M.2    Dolak, Y.3
  • 9
    • 57249084869 scopus 로고    scopus 로고
    • Large time behavior of nonlocal aggregation models with nonlinear diffusion
    • Burger M., and Di Francesco M. 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
  • 10
    • 68949158435 scopus 로고    scopus 로고
    • Fermi-Dirac-Fokker-Planck equation: Well-posedness & long-time asymptotics
    • Carrillo J.A., Laurençot P., and Rosado J. Fermi-Dirac-Fokker-Planck equation: Well-posedness & long-time asymptotics. J. Differential Equations 247 (2009) 2209-2234
    • (2009) J. Differential Equations , vol.247 , pp. 2209-2234
    • Carrillo, J.A.1    Laurençot, P.2    Rosado, J.3
  • 11
    • 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. Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana 19 (2003) 1-48
    • (2003) Rev. Mat. Iberoamericana , vol.19 , pp. 1-48
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 12
    • 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. 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    McCann, R.J.2    Villani, C.3
  • 13
    • 36549065177 scopus 로고    scopus 로고
    • 1D nonlinear Fokker-Planck equations for fermions and bosons
    • Carrillo J.A., Rosado J., and Salvarani F. 1D nonlinear Fokker-Planck equations for fermions and bosons. Appl. Math. Lett. 21 (2008) 148-154
    • (2008) Appl. Math. Lett. , vol.21 , pp. 148-154
    • Carrillo, J.A.1    Rosado, J.2    Salvarani, F.3
  • 14
    • 50849123026 scopus 로고    scopus 로고
    • A class of kinetic models for chemotaxis with threshold to prevent overcrowding
    • Chalub F.A.C.C., and Rodrigues J.F. A class of kinetic models for chemotaxis with threshold to prevent overcrowding. Port. Math. (N.S.) 63 (2006) 227-250
    • (2006) Port. Math. (N.S.) , vol.63 , pp. 227-250
    • Chalub, F.A.C.C.1    Rodrigues, J.F.2
  • 15
    • 1242299735 scopus 로고    scopus 로고
    • A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities
    • Cordero-Erausquin D., Nazaret B., and Villani C. A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Adv. Math. 182 2 (2004) 307-332
    • (2004) Adv. Math. , vol.182 , Issue.2 , pp. 307-332
    • Cordero-Erausquin, D.1    Nazaret, B.2    Villani, C.3
  • 16
    • 54349129004 scopus 로고    scopus 로고
    • Eulerian calculus for the displacement convexity in the Wasserstein distance
    • Daneri S., and Savaré G. Eulerian calculus for the displacement convexity in the Wasserstein distance. SIAM J. Math. Anal. 3 (2008) 1104-1122
    • (2008) SIAM J. Math. Anal. , vol.3 , pp. 1104-1122
    • Daneri, S.1    Savaré, G.2
  • 17
    • 33644610345 scopus 로고    scopus 로고
    • The Keller-Segel model with logistic sensitivity function and small diffusivity
    • Dolak Y., and Schmeiser C. The Keller-Segel model with logistic sensitivity function and small diffusivity. SIAM J. Appl. Math. 66 (2005) 286-308
    • (2005) SIAM J. Appl. Math. , vol.66 , pp. 286-308
    • Dolak, Y.1    Schmeiser, C.2
  • 18
    • 58149337152 scopus 로고    scopus 로고
    • Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding
    • Di Francesco M., and Rosado J. Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding. Nonlinearity 21 11 (2008) 2715-2730
    • (2008) Nonlinearity , vol.21 , Issue.11 , pp. 2715-2730
    • Di Francesco, M.1    Rosado, J.2
  • 20
    • 70450222366 scopus 로고    scopus 로고
    • Beckner inequalities and weighted transport distances
    • in preparation
    • J. Dolbeault, B. Nazaret, G. Savaré, Beckner inequalities and weighted transport distances, in preparation
    • Dolbeault, J.1    Nazaret, B.2    Savaré, G.3
  • 21
    • 1842530946 scopus 로고    scopus 로고
    • Classical Langevin equations for the free electron gas and blackbody radiation
    • Frank T.D. Classical Langevin equations for the free electron gas and blackbody radiation. J. Phys. A 37 (2004) 3561-3567
    • (2004) J. Phys. A , vol.37 , pp. 3561-3567
    • Frank, T.D.1
  • 22
    • 25644442111 scopus 로고    scopus 로고
    • Nonlinear Fokker-Planck Equations
    • Springer
    • Frank T.D. Nonlinear Fokker-Planck Equations. Springer Ser. Synergetics (2005), Springer
    • (2005) Springer Ser. Synergetics
    • Frank, T.D.1
  • 23
    • 0031116136 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits
    • Giacomin G., and Lebowitz J. Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits. J. Stat. Phys. 87 (1997) 37-61
    • (1997) J. Stat. Phys. , vol.87 , pp. 37-61
    • Giacomin, G.1    Lebowitz, J.2
  • 24
    • 0003320921 scopus 로고
    • Elliptic Problems in Nonsmooth Domains
    • Pitman (Advanced Publishing Program), Boston, MA
    • Grisvard P. Elliptic Problems in Nonsmooth Domains. Monogr. Stud. Math. vol. 24 (1985), Pitman (Advanced Publishing Program), Boston, MA
    • (1985) Monogr. Stud. Math. , vol.24
    • Grisvard, P.1
  • 25
    • 70349620978 scopus 로고    scopus 로고
    • The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
    • Gianazza U., Savaré G., and Toscani G. The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation. Arch. Ration. Mech. Anal. 194 (2009) 133-220
    • (2009) Arch. Ration. Mech. Anal. , vol.194 , pp. 133-220
    • Gianazza, U.1    Savaré, G.2    Toscani, G.3
  • 26
    • 0001404830 scopus 로고    scopus 로고
    • Global existence for a parabolic chemotaxis model with prevention of overcrowding.
    • Hillen T., and Painter K. Global existence for a parabolic chemotaxis model with prevention of overcrowding. Adv. in Appl. Math. 26 4 (2001) 280-301
    • (2001) Adv. in Appl. Math. , vol.26 , Issue.4 , pp. 280-301
    • Hillen, T.1    Painter, K.2
  • 27
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
    • Horstmann D. From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I. Jahresber. Deutsch. Math.-Verein. 105 (2003) 103-165
    • (2003) Jahresber. Deutsch. Math.-Verein. , vol.105 , pp. 103-165
    • Horstmann, D.1
  • 28
    • 0000511628 scopus 로고
    • Generalized Boltzmann equation describing the dynamics of bosons and fermions
    • Kaniadakis G. Generalized Boltzmann equation describing the dynamics of bosons and fermions. Phys. Lett. A 203 (1995) 229-234
    • (1995) Phys. Lett. A , vol.203 , pp. 229-234
    • Kaniadakis, G.1
  • 29
    • 0001544391 scopus 로고
    • Kinetic equation for classical particles obeying an exclusion principle
    • Kaniadakis G., and Quarati P. Kinetic equation for classical particles obeying an exclusion principle. Phys. Rev. E 48 (1993) 4263-4270
    • (1993) Phys. Rev. E , vol.48 , pp. 4263-4270
    • Kaniadakis, G.1    Quarati, P.2
  • 30
    • 35348914033 scopus 로고    scopus 로고
    • Characterization of absolutely continuous curves in Wasserstein spaces
    • Lisini S. Characterization of absolutely continuous curves in Wasserstein spaces. Calc. Var. Partial Differential Equations 28 (2007) 85-120
    • (2007) Calc. Var. Partial Differential Equations , vol.28 , pp. 85-120
    • Lisini, S.1
  • 33
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • McCann R.J. 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
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equation: the porous medium equation
    • Otto F. The geometry of dissipative evolution equation: 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
  • 35
    • 33746121129 scopus 로고    scopus 로고
    • Eulerian calculus for the contraction in the Wasserstein distance
    • Otto F., and Westdickenberg M. Eulerian calculus for the contraction in the Wasserstein distance. SIAM J. Math. Anal. 37 (2005) 1227-1255
    • (2005) SIAM J. Math. Anal. , vol.37 , pp. 1227-1255
    • Otto, F.1    Westdickenberg, M.2
  • 36
    • 70450223376 scopus 로고    scopus 로고
    • Existence of solutions of the hyperbolic Keller-Segel model
    • Perthame B., and Dalibard A.L. Existence of solutions of the hyperbolic Keller-Segel model. Trans. Amer. Math. Soc. 361 (2009) 2319-2335
    • (2009) Trans. Amer. Math. Soc. , vol.361 , pp. 2319-2335
    • Perthame, B.1    Dalibard, A.L.2
  • 37
    • 70350366601 scopus 로고    scopus 로고
    • Absolute continuity and summability of transport densities: Simpler proofs and new estimates
    • Santambrogio F. Absolute continuity and summability of transport densities: Simpler proofs and new estimates. Calc. Var. Partial Differential Equations 36 (2009) 343-354
    • (2009) Calc. Var. Partial Differential Equations , vol.36 , pp. 343-354
    • Santambrogio, F.1
  • 38
    • 34547422503 scopus 로고    scopus 로고
    • Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds
    • Savaré G. Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds. C. R. Math. Acad. Sci. Paris 345 (2007) 151-154
    • (2007) C. R. Math. Acad. Sci. Paris , vol.345 , pp. 151-154
    • Savaré, G.1
  • 39
    • 67650082431 scopus 로고    scopus 로고
    • Coarsening in nonlocal interfacial systems
    • Slepčev D. Coarsening in nonlocal interfacial systems. SIAM J. Math. Anal. 40 (2008) 1029-1048
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 1029-1048
    • Slepčev, D.1
  • 40
    • 33746242344 scopus 로고    scopus 로고
    • Dynamics of the Bose-Einstein condensation: Analogy with the collapse dynamics of a classical self-gravitating Brownian gas
    • Sopik J., Sire C., and Chavanis P.H. Dynamics of the Bose-Einstein condensation: Analogy with the collapse dynamics of a classical self-gravitating Brownian gas. Phys. Rev. E 74 (2006) 011112
    • (2006) Phys. Rev. E , vol.74 , pp. 011112
    • Sopik, J.1    Sire, C.2    Chavanis, P.H.3
  • 41
    • 34547843764 scopus 로고    scopus 로고
    • The Porous Medium Equation
    • Clarendon Press, Oxford University Press, Oxford
    • Vázquez J.L. The Porous Medium Equation. Oxford Math. Monogr. (2007), Clarendon Press, Oxford University Press, Oxford
    • (2007) Oxford Math. Monogr.
    • Vázquez, J.L.1
  • 42
    • 1542342359 scopus 로고    scopus 로고
    • Topics in Optimal Transportation
    • American Mathematical Society, Providence, RI
    • Villani C. Topics in Optimal Transportation. Grad. Stud. Math. vol. 58 (2003), American Mathematical Society, Providence, RI
    • (2003) Grad. Stud. Math. , vol.58
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.