About

Welcome to my webpage!

I am a postdoctoral research assistant in the field of applied mathematics in the research group of Prof. Ansgar Jüngel at the Vienna University of Technology.  My research is on partial differential equations and their applications in biology, physics, and chemistry. The focus is on the analysis, modelling and derivation of cross-diffusion in biological systems and multi-species kinetic models, moreover, I am interested in bridging PDE-techniques with probabilistic methods.

Research Interests

  • Cross diffusion in biological systems
  • Entropy methods for diffusion systems
  • Rigorous derivation from interacting stochastic particle systems
  • Uncertainty quantification
  • Hypocoercivity in kinetic equations

Publications and Preprints

Preprints

[18] E. S. Daus, J.-P. Milišić, N. Zamponi: Nonisothermal Richards flow in porous media with cross diffusion. Submitted for publication, 2021. [arXiv]

[17] L. Chen, E. S. Daus, A. Holzinger, A. Jüngel: Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems. Submitted for publication, 2020. [arXiv]

[16] E. S. Daus, M. P. Gualdani, J. Xu, N. Zamponi, X. Zhang: Non-local porous media equations with fractional time derivative. Submitted for publication, 2020. [arXiv]

[15] E. S. Daus, M. Ptashnyk, C. Raithel: Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise. Submitted for publication, 2020. [arXiv]

[14] E. S. Daus, S. Jin, L. Liu: On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation. Submitted for publication, 2019. [arXiv]

Accepted/Published Papers

[13] E. S. Daus, A. Jüngel, A. Zurek: Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms. To appear in IMA J. Numer. Anal., 2020. [DOI][arXiv]

[12] E. S. Daus, A. Jüngel, B. Q. Tang: Exponential time decay of solutions to reaction-cross-diffusion systems of Maxwell-Stefan type. Arch. Rational. Mech. Anal. 235, 2020, 1059-1104. [DOI][arXiv]

[11] E. S. Daus, M. Gualdani, N. Zamponi: Longtime behavior and weak-strong uniqueness for a nonlocal porous media equation. J. Differential Equations 268, 2020, 1820-1839. [DOI][arXiv]

[10] E. S. Daus, J.-P. Milišić, N. Zamponi: Global existence for a two-phase flow model with cross diffusion. DCDS-B, 2020, 25 (3), 957-979. [DOI] [arXiv]

[9] E. S. Daus, L. Desvillettes, A. Jüngel: Cross-diffusion systems and fast-reaction limits. Bull. Sci. Math. 159 (2020), 102824. [DOI] [arXiv]

[8] E. S. Daus, J.-P. Milišić, N. Zamponi: Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth. SIAM J. Math. Anal. 51 (2019), no. 4, 3569-3605. [DOI][arXiv]

[7] L. Chen, E. S. Daus, A. Jüngel: Rigorous mean-field limit and cross diffusion. Z. Angew. Math. Phys. 70:122, 2019. [DOI][arXiv]

[6] E. S. Daus, S. Jin, L. Liu: Spectral convergence of the stochastic Galerkin approximation to the Boltzmann equation with multiple scales and large random perturbation in the collision kernel. Kinetic & Related Models 12 (2019), no. 4, 909-922. [DOI][arXiv]

[5] E. S. Daus, L. Desvillettes, H. Dietert: About the entropic structure of detailed balanced multi-species cross-diffusion equationsJournal of  Differential Equations 266 (2019), no. 7, 3861-3882. [DOI] [arXiv]

[4] E. S. Daus, B. Q. Tang: Trend to equilibrium of renormalized solutions to reaction-cross-diffusion systems. Appl. Math. Lett. 88 (2019), 81-89. [DOI] [arXiv]

[3] X. Chen, E. S. Daus, A. Jüngel: Global existence analysis of cross-diffusion population systems for multiple species. Arch. Ration. Mech. Anal. 227 (2018), no. 2, 715-747. [DOI] [arXiv]

[2] M. Briant, E. S. Daus: The Boltzmann equation for a multi-species mixture close to global equilibrium. Arch. Ration. Mech. Anal. 222 (2016), no. 3, 1367-1443.  [DOI] [arXiv]

[1]  E. S. Daus, A. Jüngel, C. Mouhot, N. Zamponi: Hypocoercivity for a linearized multi-species Boltzmann system. SIAM J. Math. Anal. 48 (2016), no. 1, 538-568.  [DOI] [arXiv]

All papers can be found on [arXiv].

Grants and Awards

2020 Best Paper Award 2019, Faculty of Mathematics and Geoinformation, TU Wien, Austria.

2020-2022 Principal Investigator of the Multilateral Research Project Mathematical Analysis of Multispecies Fluid and Kinetic Models MULT 11/2020 between Austria, France and Serbia, OeAD Austrian Agency for International Cooperation in Education and Research, Austria.

2019 Rhine-Neckar Grant and Heidelberg Laureate Forum Foundation Travel Grant to attend the 7th Heidelberg Laureate Forum, Germany.

2019 Group Leader at the Junior Trimester Program Kinetic Theory, Hausdorff Research Institute of Mathematics Bonn, Group Stochastic-PDE Bridge, Germany.

2018-2019 Principal Investigator of the Bilateral Reserach Project Multispecies Biofilm Diffusion Systems for Wastewater Treatment HR 04/2018 between Austria and Croatia, OeAD Austrian Agency for International Cooperation in Education and Research, Austria.

2017 Christiana Hörbiger Travel Award, Austria.

2017 Best Paper Award 2016, Faculty of Mathematics and Geoinformation, TU Wien, Austria.

Organization of Events

  • Online Hausdorff School ‘Diffusive Systems’, Hausdorff School of Advanced Studies in Mathematics (HSM) Bonn, April 12-15, 2021. Organized together with Annalisa Iuorio and Cinzia Soresina. [link] [poster]
  • ‘Probabilistic and variational methods in kinetic theory’, HIM Bonn, May 13-17, 2019. Organized together with Giacomo Di Gesù and André Schlichting. [link]
  • ‘Women in PDEs@Vienna’, University of Vienna, June 17-18, 2019. Organized together with Annalisa Iuorio, Sara Merino-Aceituno and Claudia Wytrzens. [link]

Research Visits

Extended Research Visits

  • Jan-July 2017: Université Paris Diderot, Institut de Mathématiques de Jussieu- Paris Rive Gauche, Postdoc position funded by Université Sorbonne Paris Cité, France, Project with Laurent Desvillettes.

Short Research Visits

  • May-Aug. 2019: Junior Trimester Program Kinetic Theory, Hausdorff Research Institute of Mathematics, Bonn, Germany.
  •  March-June 2016, Oct-Dec 2015: Paris Université 6/7, Laboratoire Jacques-Louis Lions, Paris, France. Invited by Ayman Moussa, Laurent Boudin and Laurent Desvillettes.
  • Jan-March 2015: University of Oxford, UK
    Invited by Maria Bruna.
  • June-July 2014: University of Cambridge, UK
    Invited by Clément Mouhot.

Research Networks

  • 2020 Working group participant of the COST Program Mathematical models for interacting dynamics on networks, European Cooperation in Science and Technology. [link]