-
1
-
-
0003796630
-
-
Academic Press, London
-
R. ADAMS, Sobolev Spaces, Academic Press, London, 1975.
-
(1975)
Sobolev Spaces
-
-
Adams, R.1
-
2
-
-
31744443874
-
-
Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, Boston, Berlin
-
L. AMBROSIO, N. GIGLI, AND G. SAVARE, Gradient Flows in Metric Spaces and in the Space of Probability Measures, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, Boston, Berlin, 2005.
-
(2005)
Gradient Flows in Metric Spaces and in the Space of Probability Measures
-
-
Ambrosio, L.1
Gigli, N.2
Savare, G.3
-
3
-
-
0002042431
-
On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations
-
A. ARNOLD, P. MARKOWICH, G. TOSCANI, AND A. UNTERREITER, On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. Partial Differential Equations, 26 (2001), pp. 43-100.
-
(2001)
Comm. Partial Differential Equations
, vol.26
, pp. 43-100
-
-
Arnold, A.1
Markowich, P.2
Toscani, G.3
Unterreiter, A.4
-
4
-
-
0026929304
-
Ion flow through narrow membrane channels: part II
-
V. BARCILON, D.-P. CHEN, AND R. S. EISENBERG, Ion flow through narrow membrane channels: Part II, SIAM J. Appl. Math., 52 (1992), pp. 1405-1425. (Pubitemid 23589679)
-
(1992)
SIAM Journal on Applied Mathematics
, vol.52
, Issue.5
, pp. 1405-1425
-
-
Barcilon Victor1
Chen, D.-P.2
Eisenberg, R.S.3
-
5
-
-
49949144765
-
The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming
-
L. M. BREGMAN, The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming, USSR Comp. Math. Math. Phys., 7 (1967), pp. 200-217.
-
(1967)
USSR Comp. Math. Math. Phys.
, vol.7
, pp. 200-217
-
-
Bregman, L.M.1
-
6
-
-
37249068651
-
Inverse total variation flow
-
M. BURGER, K. FRICK, S. OSHER, AND O. SCHERZER, Inverse total variation flow, Multiscale Model. Simul., 6 (2007), pp. 366-395.
-
(2007)
Multiscale Model. Simul.
, vol.6
, pp. 366-395
-
-
Burger, M.1
Frick, K.2
Osher, S.3
Scherzer, O.4
-
7
-
-
78149424295
-
-
manuscript, WWU Münster, Münster, Germany
-
M. BURGER AND B. SCHLAKE, Nonlinear Poisson-Nernst Planck Equations for Computing Ion Flux through Confined Geometries, manuscript, WWU Münster, Münster, Germany, 2010.
-
(2010)
Nonlinear Poisson-Nernst Planck Equations for Computing Ion Flux through Confined Geometries
-
-
Burger, M.1
Schlake, B.2
-
9
-
-
18044401055
-
Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
-
J. A. CARRILLO, A. JÜNGEL, P. A. MARKOWICH, G. TOSCANI, AND A. UNTERREITER, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatsh. Math, 133 (1999), pp. 1-82.
-
(1999)
Monatsh. Math
, vol.133
, pp. 1-82
-
-
Carrillo, J.A.1
Jüngel, A.2
Markowich, P.A.3
Toscani, G.4
Unterreiter, A.5
-
10
-
-
68949158435
-
Fermi-Dirac-Fokker-Planck equation: Wellposedness and long-time asymptotics
-
J. A. CARRILLO, P. LAURENĈOT, AND J. ROSADO, Fermi-Dirac-Fokker- Planck equation: Wellposedness and long-time asymptotics, J. Differential Equations, 247 (2009), pp. 2209-2234.
-
(2009)
J. Differential Equations
, vol.247
, pp. 2209-2234
-
-
Carrillo, J.A.1
Laurenĉot, P.2
Rosado, J.3
-
11
-
-
79251515412
-
Nonlinear mobility continuity equations and generalized displacement convexity
-
to appear
-
J. A. CARRILLO, S. LISINI, G. SAVARÉ, and D. SLEPČEV, Nonlinear mobility continuity equations and generalized displacement convexity, J. Funct. Anal., (2009), to appear.
-
(2009)
J. Funct. Anal.
-
-
Carrillo, J.A.1
Lisini, S.2
Savaré, G.3
Slepčev, D.4
-
12
-
-
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), pp. 971-1018.
-
(2003)
Rev. Mat. Iberoamericana
, vol.19
, pp. 971-1018
-
-
Carrillo, J.A.1
Mccann, R.J.2
Villani, C.3
-
13
-
-
36549065177
-
1D nonlinear Fokker-Planck equations for fermions and bosons
-
J. A. CARRILLO, J. ROSADO, AND F. SALVARANI, 1D nonlinear Fokker-Planck equations for fermions and bosons, Appl. Math. Lett., 21 (2008), pp. 148-154.
-
(2008)
Appl. Math. Lett.
, vol.21
, pp. 148-154
-
-
Carrillo, J.A.1
Rosado, J.2
Salvarani, F.3
-
14
-
-
0003277699
-
Asymptotic L1-decay of solutions of the porous medium equation to self-similarity
-
J. A. CARRILLO AND G. TOSCANI, Asymptotic L1-decay of solutions of the porous medium equation to self-similarity, Indiana Univ. Math. J., 49 (2000), pp. 113-142.
-
(2000)
Indiana Univ. Math. J.
, vol.49
, pp. 113-142
-
-
Carrillo, J.A.1
Toscani, G.2
-
15
-
-
14544281036
-
Analysis of a multidimensional parabolic population model with strong cross-diffusion
-
DOI 10.1137/S0036141003427798
-
L. CHEN AND A. JÜNGEL, Analysis of a multidimensional parabolic population model with strong cross-diffusion, SIAM J. Math. Anal., 36 (2004), pp. 301-322. (Pubitemid 40305197)
-
(2005)
SIAM Journal on Mathematical Analysis
, vol.36
, Issue.1
, pp. 301-322
-
-
Chen, L.1
Jungel, A.2
-
16
-
-
33645922467
-
Analysis of a parabolic cross-diffusion population model without self-diffusion
-
L. CHEN AND A. JÜNGEL, Analysis of a parabolic cross-diffusion population model without self-diffusion, J. Differential Equations, 224 (2006), pp. 39-59.
-
(2006)
J. Differential Equations
, vol.224
, pp. 39-59
-
-
Chen, L.1
Jüngel, A.2
-
17
-
-
33847127029
-
Analysis of a parabolic cross-diffusion semiconductor model with electron-hole scattering
-
L. CHEN AND A. JÜNGEL, Analysis of a parabolic cross-diffusion semiconductor model with electron-hole scattering, Comm. Partial Differential Equations, 32 (2007), pp. 127-148.
-
(2007)
Comm. Partial Differential Equations
, vol.32
, pp. 127-148
-
-
Chen, L.1
Jüngel, A.2
-
18
-
-
0004020231
-
-
2nd ed., Clarendon Press, Oxford, UK
-
J. CRANK, The Mathematics of Diffusion, 2nd ed., Clarendon Press, Oxford, UK, 1975.
-
(1975)
The Mathematics of Diffusion
-
-
Crank, J.1
-
19
-
-
58149337152
-
Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding
-
M. DI FRANCESCO AND J. ROSADO, Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding, Nonlinearity, 21 (2008), pp. 2715-2730.
-
(2008)
Nonlinearity
, vol.21
, pp. 2715-2730
-
-
Di Francesco, M.1
Rosado, J.2
-
20
-
-
33644610345
-
The Keller-Segel model with logistic sensitivity function and small diffusivity
-
Y. DOLAK AND C. SCHMEISER, The Keller-Segel model with logistic sensitivity function and small diffusivity, SIAM J. Appl. Math., 66 (2005), pp. 286-308.
-
(2005)
SIAM, J. Appl. Math.
, vol.66
, pp. 286-308
-
-
Dolak, Y.1
Schmeiser, C.2
-
21
-
-
54349105688
-
A new class of transport distances between measures
-
J. DOLBEAULT, B. NAZARET, AND G. SAVARÉ, A new class of transport distances between measures, Calc. Var. Partial Differential Equations, 34 (2009), pp. 193-231.
-
(2009)
Calc. Var. Partial Differential Equations
, vol.34
, pp. 193-231
-
-
Dolbeault, J.1
Nazaret, B.2
Savaré, G.3
-
22
-
-
35349023238
-
Stability and other properties for nonlinear double diffusion including cross-diffusion
-
J. N. FLAVIN, M. F. MCCARTHY, AND S. RIONERO, Stability and other properties for nonlinear double diffusion including cross-diffusion, Rend. Accad. Sci. Fis.Mat. Napoli (4), 73 (2006), pp. 61-83.
-
(2006)
Rend. Accad. Sci. Fis. Mat. Napoli
, vol.4
, Issue.73
, pp. 61-83
-
-
Flavin, J.N.1
Mccarthy, M.F.2
Rionero, S.3
-
23
-
-
30844460299
-
-
Vieweg Studium, Braunschweig, Wiesbaden, Germany
-
O. FORSTER, Analysis 2, Vieweg Studium, Braunschweig, Wiesbaden, Germany, 1999.
-
(1999)
Analysis 2
-
-
Forster, O.1
-
24
-
-
2442546472
-
A parabolic cross-diffusion system for granular materials
-
G. GALIANO, A. JÜNGEL, AND J. VELASCO, A parabolic cross-diffusion system for granular materials, SIAM J. Math. Anal., 35 (2003), pp. 561-578.
-
(2003)
SIAM J. Math. Anal.
, vol.35
, pp. 561-578
-
-
Galiano, G.1
Jüngel, A.2
Velasco, J.3
-
25
-
-
0031116136
-
Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits
-
G. GIACOMIN AND J. L. LEBOWITZ, Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits, J. Statist. Phys., 87 (1997), pp. 37-61. (Pubitemid 127361673)
-
(1997)
Journal of Statistical Physics
, vol.87
, Issue.1-2
, pp. 37-61
-
-
Giacomin, G.1
Lebowitz, J.L.2
-
26
-
-
0037175732
-
Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux
-
D. GILLESPIE, W. NONNER, AND R. S. EISENBERG, Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux, J. Phys. Condens. Matter, 14 (2002), pp. 12129-12145.
-
(2002)
J. Phys. Condens. Matter
, vol.14
, pp. 12129-12145
-
-
Gillespie, D.1
Nonner, W.2
Eisenberg, S.R.3
-
28
-
-
0039712703
-
Singularity patterns in a chemotaxis model
-
M. A. HERRERO AND J. J. L. VELÁZQUEZ, Singularity patterns in a chemotaxis model, Math. Ann., 306 (1996), pp. 583-623.
-
(1996)
Math. Ann.
, vol.306
, pp. 583-623
-
-
Herrero, M.A.1
Velázquez, J.J.L.2
-
29
-
-
4744373150
-
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, Part I
-
D. HORSTMANN, From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, Part I, Jahresber. Deutsch. Math.-Verein., 105 (2003), pp. 103-165.
-
(2003)
Jahresber. Deutsch. Math.-Verein.
, vol.105
, pp. 103-165
-
-
Horstmann, D.1
-
30
-
-
13844288282
-
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, Part II
-
L. CHEN AND A. JÜNGEL, From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, Part II, Jahresber. Deutsch. Math.-Verein., 106 (2004), pp. 51-69.
-
(2004)
Jahresber. Deutsch. Math.-Verein.
, vol.106
, pp. 51-69
-
-
Chen, L.1
Jüngel, A.2
-
31
-
-
79251528149
-
Generalizing keller-segel: Multi-species chemotaxis models with attraction and repulsion between competitive interacting species
-
L. CHEN AND A. JÜNGEL, Generalizing Keller-Segel: Multi-species Chemotaxis Models with Attraction and Repulsion between Competitive Interacting Species, technical report, 2009.
-
(2009)
Technical Report
-
-
Chen, L.1
Jüngel, A.2
-
32
-
-
79251485559
-
Nonlocal elliptic boundary value problems related to chemotactic movement of mobile species
-
D. HORSTMANN AND M. LUCIA, Nonlocal elliptic boundary value problems related to chemotactic movement of mobile species, RIMS Kôkyûroku Bessatsu, B15 (2009), pp. 39-72.
-
(2009)
RIMS Kôkyûroku Bessatsu
, vol.B15
, pp. 39-72
-
-
Horstmann, D.1
Lucia, M.2
-
33
-
-
84966208077
-
On explosions of solutions to a system of partial differential equations modelling chemotaxis
-
W. JÄGER AND S. LUCKHAUS, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc., 329 (1992), pp. 819-824.
-
(1992)
Trans. Amer. Math. Soc.
, vol.329
, pp. 819-824
-
-
Jäger, W.1
Luckhaus, S.2
-
34
-
-
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), pp. 1-17.
-
(1998)
SIAM J. Math Anal.
, vol.29
, pp. 1-17
-
-
Jordan, R.1
Kinderlehrer, D.2
Otto, F.3
-
35
-
-
0014748565
-
Initiation of slime mold aggregation viewed as an instability
-
E. F. KELLER AND L. A. SEGEL, Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol., 26 (1970), pp. 399-415.
-
(1970)
J. Theoret. Biol.
, vol.26
, pp. 399-415
-
-
Keller, E.F.1
Segel, A.L.2
-
36
-
-
0003690985
-
-
AMS, Providence, RI
-
O. A. LADYZENSKAJA, V. A. SOLONNIKOV, AND N. N. URAL'CEVA, Linear and Quasilinear Equations of Parabolic Type, AMS, Providence, RI, 1968.
-
(1968)
Linear and Quasilinear Equations of Parabolic Type
-
-
Ladyzenskaja, O.A.1
Solonnikov, V.A.2
Ural'Ceva, N.N.3
-
37
-
-
85045529914
-
A chemotaxis model with threshold density and degenerate diffusion, in Nonlinear Elliptic and Parabolic Problems
-
Birkhäuser, Basel, Switzerland
-
P. LAURENĈOT AND D. WRZOSEK, A chemotaxis model with threshold density and degenerate diffusion, in Nonlinear Elliptic and Parabolic Problems, Progr. Nonlinear Differential Equations Appl. 64, Birkhäuser, Basel, Switzerland, 2005, pp. 273-290.
-
(2005)
Progr. Nonlinear Differential Equations Appl.
, vol.64
, pp. 273-290
-
-
Laurenĉot, P.1
Wrzosek, D.2
-
38
-
-
0031161793
-
A convexity principle for interacting gases
-
R. J. MCCANN, A convexity principle for interacting gases, Adv. Math., 128 (1997), pp. 153-179.
-
(1997)
Adv. Math.
, vol.128
, pp. 153-179
-
-
Mccann, R.J.1
-
39
-
-
0001560970
-
The geometry of dissipative evolution equation: The porous medium equation
-
F. OTTO, The geometry of dissipative evolution equation: The porous medium equation, Comm. Partial Differential Equations, 26 (2001), pp. 101-174.
-
(2001)
Comm. Partial Differential Equations
, vol.26
, pp. 101-174
-
-
Otto, F.1
-
40
-
-
67651113652
-
Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis
-
K. PAINTER, Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis, Bull. Math. Biol., 71 (2009), pp. 117-1147
-
(2009)
Bull. Math. Biol.
, vol.71
, pp. 117-1147
-
-
Painter, K.1
-
41
-
-
4944248574
-
Volume-filling and quorum sensing in models for chemosensitive movement
-
K. PAINTER AND T. HILLEN, Volume-filling and quorum sensing in models for chemosensitive movement, Canad. Appl. Math. Quart., 10 (2003), pp. 280-301.
-
(2003)
Canad. Appl. Math. Quart.
, vol.10
, pp. 280-301
-
-
Painter, K.1
Hillen, T.2
-
42
-
-
4944248574
-
Volume-filling and quorum-sensing in models for chemosensitive movement
-
K. J. PAINTER AND T. HILLEN, Volume-filling and quorum-sensing in models for chemosensitive movement, Canad. Appl. Math. Quart., 10 (2002), pp. 501-543.
-
(2002)
Canad. Appl. Math. Quart.
, vol.10
, pp. 501-543
-
-
Painter, K.J.1
Hillen, T.2
-
45
-
-
57349137121
-
Multi-species simple exclusion processes
-
M. SIMPSON, K. LANDMAN, AND B. HUGHES, Multi-species simple exclusion processes, Phys. A, 388 (2009), pp. 399-406.
-
(2009)
Phys. A
, vol.388
, pp. 399-406
-
-
Simpson, M.1
Landman, K.2
Hughes, B.3
-
46
-
-
9144261957
-
-
Prentice-Hall, Englewood Cliffs, NJ
-
G. TRUSKEY, F. YUAN, AND D. KATZ, Transport Phenomena in Biological Systems: International Edition, Prentice-Hall, Englewood Cliffs, NJ, 2009.
-
(2009)
Transport Phenomena in Biological Systems: International Edition
-
-
Truskey, G.1
Yuan, F.2
Katz, D.3
-
47
-
-
0001108754
-
On generalized Csiszár- Kullback inequalities
-
A. UNTERREITER, A. ARNOLD, P. MARKOWICH, AND G. TOSCANI, On generalized Csiszár- Kullback inequalities, Monatsh. Math., 131 (2000), pp. 235-253.
-
(2000)
Monatsh. Math.
, vol.131
, pp. 235-253
-
-
Unterreiter, A.1
Arnold, A.2
Markowich, P.3
Toscani, G.4
-
48
-
-
78149438591
-
-
Ph.D. Thesis, University Linz, Linz, Austria
-
M. T. WOLFRAM, Direct and Inverse Solvers for Electrodiffusion Problems, Ph.D. Thesis, University Linz, Linz, Austria, 2008.
-
(2008)
Direct and Inverse Solvers for Electrodiffusion Problems
-
-
Wolfram, M.T.1
|