Preprints

Submitted

  • C. Cancès, D. Matthes, and F. Nabet
    A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow. Submitted version.
  • D. Matthes and S. Plazotta
    A variational formulation of the BDF2 method for metric gradient flows.
    Submitted version.

Accepted/To appear

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.

Structure Preserving Discretizations

  • 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 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.
  • 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.
  • 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 version. The original publication is available at www.esaim-m2an.org.

Nonlinear Diffusion and Entropy Methods

  • 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. 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. 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.
  • 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.
  • 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, 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.
  • 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.
  • 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.

Kinetic Models

  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

Quantum Hydrodynamics

  • 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. 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.

Discrete Diffential Geometry

  • 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.
  • 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.
  • 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.

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.
 
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