Welcome to the home page of **Artur Stephan**.

I am a researcher in the group Partial Differential Equations at WIAS.

My contact details are here.

# Scientific interests

- Variational methods for evolution equations, ordinary and partial differential equations. Convex analysis and (Evolutionary) Gamma-convergence.
- Applications to classical and quantum mechanics; reaction and reaction-diffusion systems.
- Multi-scale problems and mathematical coarse-graining.
- Operator theory and semigroup theory; Markov processes; split-step approximations with convergence rate estimates.
- Numerical analysis

# Publications

You find preprints of my published papers also on arXiv. Otherwise, please contact me.

#### Submitted publications:

**A. Stephan**: "On time-splitting methods for gradient flows with two dissipation mechanisms", preprint on arXiv, July 2023.

**A. Stephan**: "Trotter-type formula for operator semigroups on product spaces", preprint on arXiv, July 2023.

**A. Stephan**, H. Stephan: "Positivity and polynomial decay of energies for square-field operators", preprint on arXiv, December 2021.

**A. Stephan**: "Coarse-graining and reconstruction for Markov matrices", preprint on arXiv, October 2021.

#### Published articles:

**A. Stephan**: "Consistency and convergence for a family of finite volume discretizations of the Fokker--Planck operator",

*ESAIM:M2AN*55.6 (2021), 25 pages, DOI:10.1051/m2an/2021078.

**A. Stephan**: "EDP-convergence for a linear reaction-diffusion system with fast reversible reaction",

*Calc. Var. PDE*60.226 (2021), 35 pages, DOI:10.1007/s00526-021-02089-0.

**A. Stephan**: "EDP-convergence for nonlinear fast-slow reaction systems with detailed balance",

*Nonlinearity*34.8 (2021), pp. 5762-5798, DOI:10.1088/1361-6544/ac0a8a.

**A. Stephan**: "Coarse-graining via EDP-convergence for linear fast-slow reaction systems",

*Math. Mod. Meth. Appl. Sci.*30.09 (2020), pp. 1765-1807, DOI:10.1142/S0218202520500360.

**A. Stephan**, V. A. Zagrebnov: "Convergence Rate Estimates for Trotter Product Approximations of Solution Operators for Non-autonomous Cauchy Problems",

*Pub. Res. I. Math. Sci.*56.1 (2020), pp. 83-135, DOI:10.4171/PRIMS/56-1-5.

**A. Stephan**, H. Stephan: "Memory equations as reduced Markov processes",

*Discr. Cont. Dyn. Systems*39.4 (2019), pp.2133-2155, DOI:10.3934/dcds.2019089.

**A. Stephan**, V. A. Zagrebnov: "Trotter Product Formula and Linear Evolution Equations on Hilbert Spaces",

*Analysis and Operator Theory. Springer Optimization and Its Applications, vol. 146*(2019), pp. 271-299, DOI:10.1007/978-3-030-12661-2_13.

**A. Stephan**, V. A. Zagrebnov: "Remarks on the operator-norm convergence of the Trotter product formula",

*Int. Equ. Op. Th.*90.15 (2018), 14 pages, DOI:10.1007/s00020-018-2424-z.

**A. Stephan**, V. A. Zagrebnov: "Operator-Norm Convergence of the Trotter Product Formula on Hilbert and Banach Spaces: A Short Survey",

*Current Research in Nonlinear Analysis. Springer Optimization and Its Applications, vol.135*(2018), pp. 229-247, DOI:10.1007/978-3-319-89800-1_9.

**A. Stephan**, V. Nekorkin: "Phase response function for oscillators with strong forcing or coupling",

*EPL (Europhysics Letters)*118.5 (2017), DOI:10.1209/0295-5075/118/50006.

**A. Stephan**, V. A. Zagrebnov: "On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations",

*Nanosystems: physics, chemistry, mathematics*8.2 (2017), pp. 202-215, DOI:10.17586/2220-8054-2017-8-2-202-215.

#### Proceedings and miscellaneous:

**A. Stephan**: "EDP-convergence for nonlinear fast-slow reaction systems",

*Oberwolfach Report 2038: Variational Methods for Evolution*(2020), DOI:10.14760/OWR-2020-29.

**A. Stephan**: "On EDP-convergence for gradient systems with different time scales",

*Proc. Appl. Math. Mech. (PAMM)*(2019), DOI:10.1002/pamm.201900366.

**A. Stephan**: "Combinatorial considerations on the invariant measure of a stochastic matrix", preprint on arXiv, (2019).

#### Theses:

**A. Stephan**:

*Coarse-graining for gradient systems and Markov processes*, Dissertation, Humboldt-Universität zu Berlin, (2021), xii + 210 pages, DOI:10.18452/23529.

**A. Stephan**:

*On operator-norm estimates for approximations of solutions of evolution equations using the Trotter product formula*, Master thesis, Humboldt-Universität zu Berlin, (2016), 69 pages, link.

# Miscellaneous

- Media

I gave a talk at the 6th BMS Student Conference on the Hamilton-Jacobi equation. The talk has been recorded.

- Membership

I am a member of the GAMM Activity Group "Analysis of Partial Differential Equations". - PhD-student representative

I was the PhD-student representative in WIAS Berlin from 2018 to 2020. - I am also on ResearchGate.

© Artur Stephan. Last modified: January 2023.