Academic Positions

• Professor (08/2010 - today)
  Extraordinarius (W2) for Dynamical Systems at the Technische Universität München
• Assistant Researcher (04/2010 - 07/2010)
  at the Technische Universität Wien
• Visiting Professor (11/2009 - 03/2010)
  Substitute (W2) for Differential Equations at the Universität Mainz
• Assistant Researcher (04/2008 - 10/2009)
  at the Technische Universität Wien
• Post-Doc Researcher (04/2007 - 03/2008)
  Assegnista di ricerca at the Università di Pavia
• Assistant Researcher (01/2004 - 03/2007)
  at the Universität Mainz

Academic Degrees

• Privatdozent (Habilitation in Applied Analysis)
  Technische Universität Wien, 14. July 2010
  "On the equilibration in certain kinetic and diffusion equations"
• Dr. rer. nat (PhD in Mathematics)
  Technische Universität Berlin, 18. December 2003
  "Discrete Surfaces and Coordinate Systems: Approximation Theorems and Computation"
• Diplom-Mathematiker (Diploma in Mathematics)
  Technische Universität Berlin, 23. July 1999
  "Analysis einer nichtlineare parabolischen Gleichung aus der Halbleiterphysik mit globaler Kopplung"

Education

• Graduate Studies (2000-2003)
  at the Technische Universität Berlin, Department of Mathematics
  PhD on discrete differential geometry (well-posedness of the initial value problem and continuous limit of discrete surfaces, coordinate systems and circle patterns)
  supervised by A.I. Bobenko/Yu.B. Suris
• Visiting Scholar (1999-2000)
  at Brown University, Providence, R.I. (USA)
  studies on perturbations of the cubic non-linear Schrödinger equation
  invited by W. Craig
• Undergraduate Studies (1995-1999)
  at the Technische Universität Berlin, Department of Mathematics
  Diploma thesis on the qualitative behaviour of a parabolic PDE (dynamical bifurcations in a reaction-diffusion equation with non-local interaction)
  supervised by R. Seiler/B. Fiedler

Preprints

• C. Cancès and D. Matthes
  Construction of a two-phase flow with singular energy by gradient flow methods.
  Preprint.
• J. Fischer and D. Matthes
  The waiting time phenomenon in spatially discretized porous medium and thin film equations.
  Preprint.
• G. Friesecke, D. Matthes, and B. Schmitzer.
  Barycenters for the Hellinger--Kantorovich distance over R^d.
  Preprint.
• J.A. Carrillo, D. Matthes, and M.-T. Wolfram
  Lagrangian schemes for Wasserstein gradient flows.
  Preprint.

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 B. Söllner
  Discretization of flux-limited gradient flows: Γ-convergence and numerical schemes.
  Math. Comp. 89 (2020), no. 323, 1027--1057.
  Preprint, Published version.
• C. Cancès, D. Matthes, and F. Nabet
  A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow.
  Arch. Ration. Mech. Anal. 233 (2019), no. 2, 837--866.
  Preprint, Published version.
• D. Matthes and S. Plazotta
  A variational formulation of the BDF2 method for metric gradient flows.
  ESAIM Math. Model. Numer. Anal. 53 (2019), no. 1, 145--172.
  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 75 (2018), no. 3, 1463--1499.
  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.
  Preprint, 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.

Theses

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.