-
1
-
-
0032343437
-
The variational formulation of the Fokker-Planck equation
-
doi:10.1137/S0036141096303359
-
Jordan R, Kinderlehrer D, Otto F. 1998 The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29, 1-17. (doi:10.1137/ S0036141096303359)
-
(1998)
SIAM J. Math. Anal.
, vol.29
, pp. 1-17
-
-
Jordan, R.1
Kinderlehrer, D.2
Otto, F.3
-
2
-
-
0032368806
-
Dynamics of Labyrinthine Pattern Formation in Magnetic Fluids: A Mean-Field Theory
-
DOI 10.1007/s002050050073
-
Otto F. 1998 Dynamics of labyrinthine pattern formation in magnetic fluids: a mean-field theory. Arch. Rational Mech. Anal. 141, 63-103. (doi:10.1007/s002050050073) (Pubitemid 128051379)
-
(1998)
Archive for Rational Mechanics and Analysis
, vol.141
, Issue.1
, pp. 63-103
-
-
Otto, F.1
-
3
-
-
0001560970
-
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 Differ. Equ. 26, 101-174. (doi:10.1081/PDE- 100002243) (Pubitemid 33731270)
-
(2001)
Communications in Partial Differential Equations
, vol.26
, Issue.1-2
, pp. 101-174
-
-
Otto, F.1
-
4
-
-
79952925967
-
A gradient structure for reaction-diffusion systems and for energy-drift- diffusion systems
-
doi:10.1088/0951-7715/24/4/016
-
Mielke A. 2011 A gradient structure for reaction-diffusion systems and for energy-drift- diffusion systems. Nonlinearity 24, 1329-1346. (doi:10.1088/0951-7715/24/4/016)
-
(2011)
Nonlinearity
, vol.24
, pp. 1329-1346
-
-
Mielke, A.1
-
5
-
-
0031161793
-
A convexity principle for interacting gases
-
DOI 10.1006/aima.1997.1634, PII S0001870897916340
-
McCann RJ. 1997 A convexity principle for interacting gases. Adv. Math. 128, 153-179. (doi:10.1006/aima.1997.1634) (Pubitemid 127171227)
-
(1997)
Advances in Mathematics
, vol.128
, Issue.1
, pp. 153-179
-
-
McCann, R.J.1
-
6
-
-
33746121129
-
Eulerian calculus for the contraction in the Wasserstein distance
-
DOI 10.1137/050622420
-
Otto F, Westdickenberg M. 2005 Eulerian calculus for the contraction in the Wasserstein distance. SIAM J. Math. Anal. 37, 1227-1255. (doi:10.1137/050622420) (Pubitemid 44085078)
-
(2005)
SIAM Journal on Mathematical Analysis
, vol.37
, Issue.4
, pp. 1227-1255
-
-
Otto, F.1
Westdickenberg, M.2
-
9
-
-
70450225042
-
Nonlinear mobility continuity equations and generalized displacement convexity
-
doi:10.1016/j.jfa.2009.10016
-
Carrillo JA, Lisini S, Savaré G, Slepcev D. 2010 Nonlinear mobility continuity equations and generalized displacement convexity. J. Funct. Anal. 258, 1273-1309. (doi:10.1016/j.jfa.2009. 10.016)
-
(2010)
J. Funct. Anal.
, vol.258
, pp. 1273-1309
-
-
Carrillo, J.A.1
Lisini, S.2
Savaré, G.3
Slepcev, D.4
-
10
-
-
54349129004
-
Eulerian calculus for the displacement convexity in the Wasserstein distance
-
doi:10.1137/08071346X
-
Daneri S, Savaré G. 2008 Eulerian calculus for the displacement convexity in the Wasserstein distance. SIAM J. Math. Anal. 40, 1104-1122. (doi:10.1137/08071346X)
-
(2008)
SIAM J. Math. Anal.
, vol.40
, pp. 1104-1122
-
-
Daneri, S.1
Savaré, G.2
-
11
-
-
0001119849
-
Diffusions hypercontractives
-
eds J Azéma, M Yor. Lecture Notes in Mathematics, 1123 Berlin Germany, Springer
-
Bakry D, Émery M. 1985 Diffusions hypercontractives. In Séminaire de probabilités, XIX, 1983/84 (eds J Azéma, M Yor), pp. 177-206. Lecture Notes in Mathematics, no. 1123. Berlin, Germany: Springer.
-
(1985)
Séminaire de Probabilités, XIX, 1983/84
, pp. 177-206
-
-
Bakry, D.1
Émery, M.2
-
12
-
-
0002925263
-
L'hypercontractivité et son utilisation en théorie des semigroupes
-
ed. P Bernard. Lecture Notes in Mathematics, 1581 Berlin Germany, Springer
-
Bakry D. 1994 L'hypercontractivité et son utilisation en théorie des semigroupes. In Lectures on probability theory (Saint-Flour, 1992) (ed. P Bernard), pp. 1-114. Lecture Notes in Mathematics, no. 1581. Berlin, Germany: Springer.
-
(1994)
Lectures on Probability Theory (Saint-Flour 1992)
, pp. 1-114
-
-
Bakry, D.1
-
14
-
-
0002042431
-
On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations
-
Arnold A, Markowich P, Toscani G, Unterreiter A. 2001 On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Commun. Partial Differ. Equ. 26, 43-100. (doi:10.1081/PDE-100002246) (Pubitemid 33731269)
-
(2001)
Communications in Partial Differential Equations
, vol.26
, Issue.1-2
, pp. 43-100
-
-
Arnold, A.1
Markowich, P.2
Toscani, G.3
Unterreiter, A.4
-
15
-
-
79960891765
-
Gradient flows of the entropy for finite Markov chains
-
doi:10.1016/j.jfa.2011.06.009
-
Maas J. 2011 Gradient flows of the entropy for finite Markov chains. J. Funct. Anal. 261, 2250-2292. (doi:10.1016/j.jfa.2011.06.009)
-
(2011)
J. Funct. Anal.
, vol.261
, pp. 2250-2292
-
-
Maas, J.1
-
16
-
-
84881611840
-
Geodesic convexity of the relative entropy in reversible Markov chains
-
doi:10.1007/s00526-012-0538-8
-
Mielke A. 2012 Geodesic convexity of the relative entropy in reversible Markov chains. Calc. Var. Part. Differ. Equ. 48, 1-31. (doi:10.1007/s00526-012- 0538-8)
-
(2012)
Calc. Var. Part. Differ. Equ.
, vol.48
, pp. 1-31
-
-
Mielke, A.1
-
17
-
-
84868145916
-
Ricci curvature of finite Markov chains via convexity of the entropy
-
doi:10.1007/s00205-012-0554-z
-
Erbar M, Maas J. 2012 Ricci curvature of finite Markov chains via convexity of the entropy. Arch. Ration. Mech. Anal. 206, 997-1038. (doi:10.1007/s00205-012-0554-z)
-
(2012)
Arch. Ration. Mech. Anal.
, vol.206
, pp. 997-1038
-
-
Erbar, M.1
Maas, J.2
-
18
-
-
68549126882
-
Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces
-
doi:10.1051/cocv:2008044
-
Lisini S. 2009 Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces. ESAIM Control Optim. Calc. Var. 15, 712-740. (doi:10.1051/cocv:2008044)
-
(2009)
ESAIM Control Optim. Calc. Var.
, vol.15
, pp. 712-740
-
-
Lisini, S.1
-
19
-
-
74949092030
-
A family of nonlinear fourth order equations of gradient flow type
-
doi101080/03605300903296256
-
Matthes D, McCann RJ, Savaré G. 2009 A family of nonlinear fourth order equations of gradient flow type. Commun. Partial Differ. Equ. 34, 1352-1397. (doi:10.1080/0360530090 3296256)
-
(2009)
Commun. Partial Differ. Equ.
, vol.34
, pp. 1352-1397
-
-
Matthes, D.1
McCann, R.J.2
Savaré, G.3
-
20
-
-
70349620978
-
The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
-
doi:10.1007/s00205-008-0186-5
-
Gianazza U, Savaré G, Toscani G. 2009 The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation. Arch. Rational Mech. Anal. 194, 133-220. (doi:10.1007/s00205-008-0186-5)
-
(2009)
Arch. Rational Mech. Anal.
, vol.194
, pp. 133-220
-
-
Gianazza, U.1
Savaré, G.2
Toscani, G.3
-
21
-
-
84860635892
-
Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics
-
doi:10.1016/j.jde.2012.04.004
-
Lisini S, Matthes D, Savaré G. 2012 Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. J. Differ. Equ. 253, 814-850. (doi:10.1016/j.jde.2012.04.004)
-
(2012)
J. Differ. Equ.
, vol.253
, pp. 814-850
-
-
Lisini, S.1
Matthes, D.2
Savaré, G.3
-
23
-
-
77954540383
-
A new transportation distance between non-negative measures, with applications to gradient flows with Dirichlet boundary conditions
-
doi:10.1016/j.matpur.2009.11.005
-
Figalli A, Gigli N. 2010 A new transportation distance between non-negative measures, with applications to gradient flows with Dirichlet boundary conditions. J. Math. Pures Appl. 94, 107-130. (doi:10.1016/j.matpur. 2009.11.005)
-
(2010)
J. Math. Pures Appl.
, vol.94
, pp. 107-130
-
-
Figalli, A.1
Gigli, N.2
-
25
-
-
2442651888
-
Entropic structure of multicomponent reactive flows with partial equilibrium reduced chemistry
-
doi:10.1002/mma.429
-
Giovangigli V, Massot M. 2004 Entropic structure of multicomponent reactive flows with partial equilibrium reduced chemistry. Math. Methods Appl. Sci. (MMAS) 27, 739-768. (doi:10.1002/mma.429)
-
(2004)
Math. Methods Appl. Sci. (MMAS)
, vol.27
, pp. 739-768
-
-
Giovangigli, V.1
Massot, M.2
-
27
-
-
34547932449
-
Global existence for quadratic systems of reaction-diffusion
-
Desvillettes L, Fellner K, Pierre M, Vovelle J. 2007 Global existence for quadratic systems of reaction-diffusion. Adv. Nonlinear Stud. 7, 491-511.
-
(2007)
Adv. Nonlinear Stud.
, vol.7
, pp. 491-511
-
-
Desvillettes, L.1
Fellner, K.2
Pierre, M.3
Vovelle, J.4
-
28
-
-
54049156080
-
Entropy methods for reaction-diffusion equations: Slowly growing a-priori bounds
-
doi:10.4171/RMI/541
-
Desvillettes L, Fellner K. 2008 Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds. Rev. Mat. Iberoam. 24, 407-431. (doi:10.4171/RMI/541)
-
(2008)
Rev. Mat. Iberoam.
, vol.24
, pp. 407-431
-
-
Desvillettes, L.1
Fellner, K.2
-
29
-
-
22544468527
-
Global existence result for pair diffusion models
-
DOI 10.1137/S0036141002417590
-
Glitzky A, Hünlich R. 2005 Global existence result for pair diffusion models. SIAM J. Math. Anal. 36, 1200-1225. (doi:10.1137/ S0036141002417590) (Pubitemid 41013544)
-
(2005)
SIAM Journal on Mathematical Analysis
, vol.36
, Issue.4
, pp. 1200-1225
-
-
Glitzky, A.1
Hunlich, R.2
-
30
-
-
33645548609
-
Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations
-
DOI 10.1016/j.jmaa.2005.07.003, PII S0022247X05006773
-
Desvillettes L, Fellner K. 2006 Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations. J. Math. Anal. Appl. 319, 157-176. (doi:10.1016/j.jmaa.2005. 07.003) (Pubitemid 43506852)
-
(2006)
Journal of Mathematical Analysis and Applications
, vol.319
, Issue.1
, pp. 157-176
-
-
Desvillettes, L.1
Fellner, K.2
-
31
-
-
59049085863
-
Entropy methods for reaction-diffusion systems
-
doi:10.3934/proc.2007.2007.304
-
Desvillettes L, Fellner K. 2007 Entropy methods for reaction-diffusion systems. Discrete Cont. Dyn. Syst. Suppl. 2007, 304-312. (doi:10.3934/proc.2007. 2007.304)
-
(2007)
Discrete Cont. Dyn. Syst. Suppl.
, vol.2007
, pp. 304-312
-
-
Desvillettes, L.1
Fellner, K.2
-
32
-
-
70349847395
-
Energy estimates for electro-reaction-diffusion systems with partly fast kinetics
-
doi:10.3934/dcds.2009.25.159
-
Glitzky A. 2009 Energy estimates for electro-reaction-diffusion systems with partly fast kinetics. Discrete Cont. Dyn. Syst. Ser. A 25, 159-174. (doi:10.3934/dcds.2009.25.159)
-
(2009)
Discrete Cont. Dyn. Syst. Ser. A
, vol.25
, pp. 159-174
-
-
Glitzky, A.1
-
33
-
-
84864480696
-
The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction
-
doi:10.3934/dcdss.2012.5.49
-
Bothe D, Pierre M. 2011 The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction. Discrete Cont. Dyn. Syst. Ser. S 8, 49-59. (doi:10.3934/dcdss.2012.5.49)
-
(2011)
Discrete Cont. Dyn. Syst. Ser. S
, vol.8
, pp. 49-59
-
-
Bothe, D.1
Pierre, M.2
-
34
-
-
84873524513
-
A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces
-
doi:10.1007/S00033-012-0207-y
-
Glitzky A,Mielke A. 2013 A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Z. Angew. Math. Phys. 64, 29-52. (doi:10.1007/S00033-012-0207-y)
-
(2013)
Z. Angew. Math. Phys.
, vol.64
, pp. 29-52
-
-
Glitzky Amielke, A.1
-
35
-
-
84874172898
-
Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions
-
doi:10.3934/dcdss. 2013.6.479
-
Mielke A. 2013 Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Discrete Contin. Dyn. Syst. Ser. S 6, 479-499. (doi:10.3934/dcdss. 2013.6.479)
-
(2013)
Discrete Contin. Dyn. Syst. Ser. S
, vol.6
, pp. 479-499
-
-
Mielke, A.1
-
36
-
-
79956131596
-
Formulation of thermoelastic dissipative material behavior using GENERIC
-
doi:10.1007/s00161-010-0179-0
-
Mielke A. 2011 Formulation of thermoelastic dissipative material behavior using GENERIC. Contin. Mech. Thermodyn. 23, 233-256. (doi:10.1007/s00161-010- 0179-0)
-
(2011)
Contin. Mech. Thermodyn.
, vol.23
, pp. 233-256
-
-
Mielke, A.1
-
37
-
-
0042974062
-
Thermodynamic design of energy models of semiconductor devices
-
DOI 10.1088/0951-7715/15/2/307, PII S0951771502224858
-
Albinus G, Gajewski H, Hünlich R. 2002 Thermodynamic design of energy models of semiconductor devices. Nonlinearity 15, 367-383. (doi:10.1088/0951-7715/15/2/307) (Pubitemid 37023524)
-
(2002)
Nonlinearity
, vol.15
, Issue.2
, pp. 367-383
-
-
Albinus, G.1
Gajewski, H.2
Hunlich, R.3
-
39
-
-
0001835099
-
Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems
-
eds H-J Schmeisser, H Triebel. Teubner-Texte Math. 133 Stuttgart Germany Teubner
-
Amann H. 1993 Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In Function spaces, differential operators and nonlinear analysis (eds H-J Schmeisser, H Triebel), pp. 9-126. Teubner-Texte Math., no. 133. Stuttgart, Germany: Teubner.
-
(1993)
Function Spaces, Differential Operators and Nonlinear Analysis
, pp. 9-126
-
-
Amann, H.1
-
40
-
-
53649085750
-
A gradient flow approach to an evolution problem arising in superconductivity
-
doi:10.1002/cpa.20223
-
Ambrosio L, Serfaty S. 2008 A gradient flow approach to an evolution problem arising in superconductivity. Commun. Pure Appl. Math. 61, 1495-1539. (doi:10.1002/cpa.20223)
-
(2008)
Commun. Pure Appl. Math.
, vol.61
, pp. 1495-1539
-
-
Ambrosio, L.1
Serfaty, S.2
-
41
-
-
0034407460
-
A computational fluid mechanics solution to the Monge- Kantorovich mass transfer problem
-
doi:10.1007/s002110050002
-
Benamou J-D, Brenier Y. 2000 A computational fluid mechanics solution to the Monge- Kantorovich mass transfer problem. Numer. Math. 84, 375-393. (doi:10.1007/s002110050002)
-
(2000)
Numer. Math.
, vol.84
, pp. 375-393
-
-
Benamou, J.-D.1
Brenier, Y.2
-
43
-
-
51849095782
-
Exponential decay of the free energy for discretized electro-reaction- diffusion systems
-
doi:10.1088/0951-7715/21/9/003
-
Glitzky A. 2008 Exponential decay of the free energy for discretized electro-reaction-diffusion systems. Nonlinearity 21, 1989-2009. (doi:10.1088/0951-7715/21/9/003)
-
(2008)
Nonlinearity
, vol.21
, pp. 1989-2009
-
-
Glitzky, A.1
-
44
-
-
56149083866
-
Energy estimates for continuous and discretized electro-reaction- diffusion systems
-
doi:10.1016/j.na.2008.01.015
-
Glitzky A, Gärtner K. 2009 Energy estimates for continuous and discretized electro-reaction- diffusion systems. Nonlinear Anal. 70, 788-805. (doi:10.1016/j.na.2008.01.015)
-
(2009)
Nonlinear Anal.
, vol.70
, pp. 788-805
-
-
Glitzky, A.1
Gärtner, K.2
-
47
-
-
79251530502
-
Nonlinear cross-diffusion with size exclusion
-
doi:10.1137/100783674
-
Burger M, Di Franscesco M, Pietschmann J-F, Schlake B. 2010 Nonlinear cross-diffusion with size exclusion. SIAM J. Math. Anal. 42, 2842-2871. (doi:10.1137/100783674)
-
(2010)
SIAM J. Math. Anal.
, vol.42
, pp. 2842-2871
-
-
Burger, M.1
Di Franscesco, M.2
Pietschmann, J.-F.3
Schlake, B.4
-
48
-
-
27744454983
-
On the unique solvability of a nonlocal phase separation problem for multicomponent systems
-
eds P Biler, G Karch, TNadzieja. Banach Center Publication, no. 66.Warsaw, Poland: Polish Academy of Science
-
Griepentrog JA. 2004 On the unique solvability of a nonlocal phase separation problem for multicomponent systems. In Nonlocal elliptic and parabolic problems (eds P Biler, G Karch, TNadzieja), pp. 153-164. Banach Center Publication, no. 66.Warsaw, Poland: Polish Academy of Science.
-
(2004)
Nonlocal Elliptic and Parabolic Problems
, pp. 153-164
-
-
Griepentrog, J.A.1
|