### Preprints

• C. Cancès, D. Matthes, and F. Nabet
A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow.
Submitted version.

### Published Papers

Note: Due to the usual issues with the copyright, the preprints provided for download below are not fully identical to the eventually published papers. In some cases, there is a significant difference with respect to presentation, mathematical correctness and completeness of references.

• D. Matthes and S. Plazotta
A variational formulation of the BDF2 method for metric gradient flows.
Preprint, Published version.
• J.A. Carrillo, B. Düring, D. Matthes, and D.S. McCormick.
A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes.
Journal of Scientific Computing (2017).
Preprint, Published Version.
• O. Junge, D. Matthes, and H. Osberger.
A fully discrete variational scheme for solving nonlinear Fokker-Planck equations in multiple space dimensions.
SIAM J. Numer. Anal. 55 (2017), no. 1, 419--443.
Preprint, Published version.
• D. Matthes and J. Zinsl.
Existence of solutions for a class of fourth order cross-diffusion systems of gradient flow type.
Nonlinear Analysis 159 (2017), 316--338.
Submitted version, Published version.
• D. Matthes and B. Söllner.
Convergent Lagrangian discretization for drift-diffusion with nonlocal aggregation.
Chapter in: "Innovate Algorithms and Analysis", 313--351.
Edited by L. Gosse et al., Springer INdAM series 16 (2017).
Preprint,Entire collection.
• A. Denner, O. Junge, and D. Matthes.
Computing coherent sets using the Fokker-Planck equation.
Journal of Computational Dynamics 3 (2016), no. 2, 163--177.
Preprint, Published version.
• U. Bücking and D. Matthes.
Constructing solutions to the Björling problem for isothermic surfaces by structure preserving discretization.
Chapter in "Advances in Discrete Differential Geometry", 309--346.
Edited by A.I. Bobenko (Springer 2016).
Preprint version, Entire collection.
• D. Loibl, D. Matthes, and J. Zinsl.
Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient flow structure.
Potential Analysis 45 (2016), no. 4, 755-776.
Preprint, Published version.
• J.-F. Mennemann, D. Matthes, R.M. Weishäupl, and T. Langen.
Optimal control of Bose-Einstein condensates in three dimensions.
New Journal of Physics 17 (2015), 113027.
Preprint, Published version.
• J. Maas and D. Matthes.
Long-time behavior of a finite volume discretization for a fourth order diffusion equation.
Nonlinearity 29 (2016), no. 7, 1992.
Preprint, Published version.
• H. Osberger and D. Matthes.
Convergence of a fully discrete variational scheme for a thin-film equation.
Radon Ser. Comput. Appl. Math. 18 (2017), 356--399.
Preprint, Published version.
• D. Matthes and H. Osberger.
A convergent Lagrangian discretization for a nonlinear fourth order equation.
Found. Comput. Math. 17 (2017), no. 1, 73-–126.
Preprint, Published version.
• 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.
Preprint, Published version.
• J. Zinsl and D. Matthes.
Exponential convergence to equilibrium in a gradient flow system modeling chemotaxis.
Analysis and PDE 8 (2015), no. 2, 256--466.
Preprint, Published version.
• F. Bassetti, L. Ladelli, and D. Matthes.
Infinite energy solutions to inelastic homogeneous Boltzmann equations.
Electron. J. Probab. 20 (2015), no. 89, 1--34.
Preprint version, Published version.
• D. Matthes and H. Osberger.
Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation.
ESAIM Math. Model. Numer. Anal. 48 (2014), 697--726.
Preprint, Published version.
• F. Bassetti and D. Matthes.
Multi-dimensional smoothing transformations: existence, regularity and stability of fixed points.
Stochastic Process. Appl. 124 (2014), no. 1, 154--198.
Preprint, Published version.
• M. Di Francesco, M. Fornasier, J.C. Hütter, and D. Matthes.
Asymptotic behavior of gradient flows driven by nonlocal power repulsion and attraction potentials in one dimension.
SIAM J. Math. Anal. 46 (2014), no. 6, 3814--3837.
Preprint, Published version.
• M. Di Francesco and D. Matthes.
Curves of steepest descent are entropy solutions for a class of degenerate convection-diffusion equations.
Calc. Var. Partial Differential Equations 50 (2014), no. 1, 199--230.
Preprint, Published version.
• M. Bukal, A. Jüngel, and D. Matthes.
A multidimensional nonlinear sixth-order quantum diffusion equation.
Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 2, 337-365.
Preprint, Published version.
• 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.
Preprint, Published version.
• D. Matthes and G. Toscani.
Variation on a theme by Bobylev and Villani.
C. R. Math. Acad. Sci. Paris 350 (2012), no. 1-2, 107--110.
Preprint, Published version.
• M. Bukal, A. Jüngel, and D. Matthes.
Entropies for radially symmetric higher-order nonlinear diffusion equations.
Commun. Math. Sci. 9 (2011), no. 2, 353--382.
Preprint, Published version.
• B. Düring, D. Matthes, and P. Milisic.
A gradient flow scheme for nonlinear fourth order equations.
Discrete Contin. Dyn. Syst. Ser. B 14 (2010), no. 3, 935--959.
Preprint, Published version.
• D. Matthes and G. Toscani.
Propagation of Sobolev regularity for a class of random kinetic models on the real line.
Nonlinearity 23 (2010), no. 9, 2081.
Preprint, Published version.
• D. Matthes, A. Jüngel, and G. Toscani.
Convex Sobolev inequalities derived from entropy dissipation.
Arch. Ration. Mech. Anal. 199 (2011), no. 2, 563--596.
Preprint, Published version.
• F. Bassetti, L. Ladelli, and D. Matthes.
Central limit theorem for a class of one-dimensional kinetic equations.
Prob. Theory Related Fields 150 (2010), no. 1-2, 77--109.
Preprint, Published version.
• D. Matthes, R. J. McCann, and G. Savaré.
A family of fourth order equations of gradient flow type.
Comm. P.D.E. 34 (2009), no. 11, 1352--1397.
Preprint, Published version.
• B. Düring, D. Matthes, and G. Toscani.
Kinetic equations modelling wealth redistribution: a comparison of approaches.
Phys. Rev. E 78 (2008), no. 5, 050801.
Preprint, Published version.
• D. Matthes and G. Toscani.
Analysis of a model for wealth redistribution.
Kinet. Relat. Models 1 (2008), no. 1, 1--27.
Preprint, Published version.
• D. Matthes and G. Toscani.
On steady distributions of kinetic models of conservative economies.
J. Stat. Phys. 130 (2008), no. 6, 1087--1117.
Preprint, Published version.
• P. Amster, A. Jüngel, and D. Matthes.
Non-homogeneous boundary conditions for a fourth-order diffusion equation.
C. R. Math. Acad. Sci. Paris 346 (2008), no. 3-4, 143--148.
Preprint, Published version.
• A. Jüngel and D. Matthes.
The Derrida-Lebowitz-Speer-Spohn equation: existence, non-uniqueness, and decay rates of the solutions.
SIAM J. Math. Anal. 39 (2008), no. 6, 1996--2015.
Preprint, Published version.
• A. Jüngel and D. Matthes.
An algorithmic construction of entropies in higher-order nonlinear PDEs.
Nonlinearity 19 (2006), no. 3, 633--659.
Preprint, Published version.
• A. Jüngel, D. Matthes, and J.P. Milisic.
Derivation of new quantum hydrodynamic equations using entropy minimization.
SIAM J. Appl. Math. 67 (2006), no. 1, 46--68.
Preprint, Published version.
• A.I. Bobenko, D. Matthes, and Yu.B. Suris.
Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results.
St. Petersburg Math. J. 17 (2006), no. 1, 39--61.
Preprint, Published version.
• A. Jüngel and D. Matthes.
A derivation of the isothermal quantum hydrodynamic equations using entropy minimization.
ZAMM Z. Angew. Math. Mech. 85 (2005), no. 11, 806--814.
Preprint, Published version.
• D. Matthes. Convergence in discrete Cauchy problems and applications to circle patterns.
Conform. Geom. Dyn. 9 (2005), 1--23.
Preprint, Published version.
• A.I. Bobenko, D. Matthes, and Yu.B. Suris.
Discrete and smooth orthogonal systems: $C\sp \infty$-approximation.
Int. Math. Res. Not. 45 (2003), 2415--2459.
Preprint, Published version.

### Proceedings and reviews

• B. Düring and D. Matthes.
A mathematical theory for wealth distribution.
In: "Mathematical modeling of collective behavior in socio-economic and life-sciences."
(Edited by G. Naldi et al.) Birkhäuser, Boston 2010, 81--113.
Preprint, Published version.
• B. Düring, D. Matthes, and G. Toscani.
A Boltzmann-type approach to the formation of wealth distribution curves.
Rivista di Matematica Università di Parma 8 (2009), no. 1, 199--261.
Preprint, Published version.
• A. Jüngel and D. Matthes.
Entropiemethoden für nichtlineare partielle Differentialgleichungen.
Internationale Mathematische Nachrichten 209 (2008), 1--14.
Preprint, Published version.

• Daniel Matthes, joint with S. Plazotta.
A two-step time discetization of metric gradient flows.
Oberwolfach reports 14 (2017), no. 4.
Preprint, Published version.
• D. Matthes, joint with J. Zinsl.
Systems of diffusion equations as gradient flows in multi-component transportation metrics.
Oberwolfach Reports 11 (2014), no. 4.
Preprint, Published version.
• D. Matthes, joint with F. Bassetti and L. Ladelli.
Infinite energy solutions for a homogeneous inelastic Maxwell gas.
Oberwolfach Reports 10 (2013), no. 4.
Preprint, Published version.
• D. Matthes.
Kinetic models with non-strict conservations.
Oberwolfach Reports 7 (2010), no. 4, 3200--3203.
Preprint, Published version.
• B. Düring, D. Matthes, and G.Toscani.
Exponential and algebraic relaxation in kinetic models for wealth distribution.
Proceedings WASCOM 2007, World Scientific, Singapore 2008, 228--238.
Preprint.
• A. Jüngel and D. Matthes.
A review on results for the Derrida-Lebowitz-Speer-Spohn equation.
Submitted to Proceedings of the EquaDiff 2007.
Preprint.

### Lecture Notes

• D. Matthes.
Entropy methods and related functional inequalities.
Lecture notes from the course given in Pavia winter term 2007/2008.

## Doctoral Thesis

• Supervised by A.I. Bobenko
Discrete Surfaces and Coordinate Systems: Approximation Theorems and Computation.
Published online by the Technische Universität Berlin. PhD defense 12.12.2003.

## Diploma Thesis

• Supervised by R. Seiler.
Analysis einer nichtlinearen parabolischen Gleichung aus der Halbleiterphysik mit globaler Kopplung.
Diploma completed 23.6.1999.