[1]

L. Ambrosio, N. Gigli and G. Savaré,
Gradient Flows in Metric Spaces and in the Space of Probability Measures, 2nd ed.,
Lectures in Math. ETH Zürich,
Birkhäuser, Basel, 2008.
Google Scholar

[2]

B. Aulbach and N. V. Minh,
Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations,
Abstr. Appl. Anal. 1 (1996), no. 4, 351–380.
CrossrefGoogle Scholar

[3]

J.-P. Bartier, J. Dolbeault, R. Illner and M. Kowalczyk,
A qualitative study of linear drift-diffusion equations with time-dependent or degenerate coefficients,
Math. Models Methods Appl. Sci. 17 (2007), no. 3, 327–362.
Web of ScienceCrossrefGoogle Scholar

[4]

J.-D. Benamou and Y. Brenier,
A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem,
Numer. Math. 84 (2000), no. 3, 375–393.
CrossrefGoogle Scholar

[5]

A. Blanchet, J. A. Carrillo, D. Kinderlehrer, M. Kowalczyk, P. Laurençot and S. Lisini,
A hybrid variational principle for the Keller–Segel system in ${\mathbb{R}}^{2}$,
ESAIM Math. Model. Numer. Anal. 49 (2015), no. 6, 1553–1576.
Google Scholar

[6]

J. A. Carrillo, S. Lisini, G. Savaré and D. Slepčev,
Nonlinear mobility continuity equations and generalized displacement convexity,
J. Funct. Anal. 258 (2010), no. 4, 1273–1309.
CrossrefWeb of ScienceGoogle Scholar

[7]

S. Daneri and G. Savaré,
Eulerian calculus for the displacement convexity in the Wasserstein distance,
SIAM J. Math. Anal. 40 (2008), no. 3, 1104–1122.
CrossrefWeb of ScienceGoogle Scholar

[8]

J. Dolbeault, B. Nazaret and G. Savaré,
A new class of transport distances between measures,
Calc. Var. Partial Differential Equations 34 (2009), no. 2, 193–231.
CrossrefWeb of ScienceGoogle Scholar

[9]

L. C. F. Ferreira and J. C. Valencia-Guevara,
Gradient flows of time-dependent functionals in metric spaces and applications for PDEs,
preprint (2015), https://arxiv.org/abs/1509.04161.

[10]

U. Gianazza, G. Savaré and G. Toscani,
The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation,
Arch. Ration. Mech. Anal. 194 (2009), no. 1, 133–220.
Web of ScienceCrossrefGoogle Scholar

[11]

R. Jordan, D. Kinderlehrer and F. Otto,
The variational formulation of the Fokker–Planck equation,
SIAM J. Math. Anal. 29 (1998), no. 1, 1–17.
CrossrefGoogle Scholar

[12]

P. Laurençot and B.-V. Matioc,
A gradient flow approach to a thin film approximation of the Muskat problem,
Calc. Var. Partial Differential Equations 47 (2013), no. 1–2, 319–341.
Web of ScienceCrossrefGoogle Scholar

[13]

D. Lengeler and T. Müller,
Scalar conservation laws on constant and time-dependent Riemannian manifolds,
J. Differential Equations 254 (2013), no. 4, 1705–1727.
CrossrefWeb of ScienceGoogle Scholar

[14]

M. Liero and A. Mielke,
Gradient structures and geodesic convexity for reaction-diffusion systems,
Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 371 (2013), no. 2005, Article ID 20120346.
Google Scholar

[15]

S. Lisini,
Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces,
ESAIM Control Optim. Calc. Var. 15 (2009), no. 3, 712–740.
CrossrefWeb of ScienceGoogle Scholar

[16]

S. Lisini and A. Marigonda,
On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals,
Manuscripta Math. 133 (2010), no. 1–2, 197–224.
CrossrefWeb of ScienceGoogle Scholar

[17]

S. Lisini, D. Matthes and G. Savaré,
Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics,
J. Differential Equations 253 (2012), no. 2, 814–850.
Web of ScienceCrossrefGoogle Scholar

[18]

D. Loibl, D. Matthes and J. Zinsl,
Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure,
Potential Anal. 45 (2016), no. 4, 755–776.
CrossrefWeb of ScienceGoogle Scholar

[19]

D. Matthes, R. J. McCann and G. Savaré,
A family of nonlinear fourth order equations of gradient flow type,
Comm. Partial Differential Equations 34 (2009), no. 10–12, 1352–1397.
CrossrefGoogle Scholar

[20]

R. J. McCann,
A convexity principle for interacting gases,
Adv. Math. 128 (1997), no. 1, 153–179.
CrossrefGoogle Scholar

[21]

F. Otto,
The geometry of dissipative evolution equations: The porous medium equation,
Comm. Partial Differential Equations 26 (2001), no. 1–2, 101–174.
CrossrefGoogle Scholar

[22]

L. Petrelli and A. Tudorascu,
Variational principle for general diffusion problems,
Appl. Math. Optim. 50 (2004), no. 3, 229–257.
CrossrefGoogle Scholar

[23]

S. Plazotta and J. Zinsl,
High-frequency limit of non-autonomous gradient flows of functionals with time-periodic forcing,
J. Differential Equations 261 (2016), no. 12, 6806–6855.
Web of ScienceCrossrefGoogle Scholar

[24]

R. Rossi and G. Savaré,
Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 2, 395–431.
Google Scholar

[25]

K.-T. Sturm,
Super-Ricci flows for metric measure spaces. I,
preprint (2016), https://arxiv.org/abs/1603.02193.

[26]

C. Villani,
Topics in Optimal Transportation,
Grad. Stud. Math. 58,
American Mathematical Society, Providence, 2003.
Google Scholar

[27]

J. Zinsl,
Existence of solutions for a nonlinear system of parabolic equations with gradient flow structure,
Monatsh. Math. 174 (2014), no. 4, 653–679.
Web of ScienceCrossrefGoogle Scholar

[28]

J. Zinsl,
The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances,
Discrete Contin. Dyn. Syst. Ser. S 10 (2017), no. 4, 919–933.
Web of ScienceGoogle Scholar

[29]

J. Zinsl and D. Matthes,
Transport distances and geodesic convexity for systems of degenerate diffusion equations,
Calc. Var. Partial Differential Equations 54 (2015), no. 4, 3397–3438.
Web of ScienceCrossrefGoogle Scholar

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.