Research Interests

Research Interests

$\bullet$ Nonlinear dynamics of partial/ordinary differential equations and stochastic processes
$\bullet$ long-time asymptotics: metastability, phase-transitions and coarsening
$\bullet$ Interacting particle system and their scaling limits
$\bullet$ Variational methods for evolution equations: gradient flows and optimal transport
$\bullet$ Structure preserving numerical schemes

Current Cluster Publications

Current Cluster Publications of Prof. Dr. André Schlichting

$\bullet $ Chun Yin Lam and André Schlichting. Variational convergence of exchange-driven stochastic particle systems in the thermodynamic limit. arXiv e-prints, January 2024. arXiv:2401.06696.

$\bullet $ Daniel Matthes, Eva-Maria Rott, Giuseppe Savaré, and André Schlichting. A structure preserving discretization for the Derrida-Lebowitz-Speer-Spohn equation based on diffusive transport. arXiv e-prints, December 2023. arXiv:2312.13284.

$\bullet $ Víctor Navarro-Fernández and André Schlichting. Error estimates for a finite volume scheme for advection–diffusion equations with rough coefficients. ESAIM: Mathematical Modelling and Numerical Analysis, 57(4):2131–2158, July 2023. doi:10.1051/m2an/2023035.

$\bullet $ Antonio Esposito, Georg Heinze, Jan-Frederik Pietschmann, and André Schlichting. Graph-to-local limit for a multi-species nonlocal cross-interaction system. arXiv e-prints, June 2023. arXiv:2306.17414.

$\bullet $ Anastasiia Hraivoronska, André Schlichting, and Oliver Tse. Variational convergence of the Scharfetter-Gummel scheme to the aggregation-diffusion equation and vanishing diffusion limit. arXiv e-prints, June 2023. arXiv:http://arxiv.org/abs/2306.02226.

$\bullet $ Antonio Esposito, Georg Heinze, and André Schlichting. Graph-to-local limit for the nonlocal interaction equation. arXiv e-prints, June 2023. arXiv:2306.03475.

$\bullet $ Antonio Esposito, Francesco Saverio Patacchini, and André Schlichting. On a class of nonlocal continuity equations on graphs. European Journal of Applied Mathematics, 35(1):109–126, May 2023. doi:10.1017/S0956792523000128.

$\bullet $ Martin Burger, Matthias Erbar, Franca Hoffmann, Daniel Matthes, and André Schlichting. Covariance-modulated optimal transport and gradient flows. arXiv e-prints, February 2023. arXiv:2302.07773.

$\bullet $ Víctor Navarro-Fernández, André Schlichting, and Christian Seis. Optimal stability estimates and a new uniqueness result for advection-diffusion equations. Pure and Applied Analysis, 4(3):571–596, December 2022. doi:10.2140/paa.2022.4.571.

$\bullet $ Antonio Esposito, Francesco S. Patacchini, and André Schlichting. On a class of nonlocal continuity equations on graphs. arXiv e-prints, September 2022. arXiv:2209.15552.

$\bullet $ Georg Menz, André Schlichting, Wenpin Tang, and Tianqi Wu. Ergodicity of the infinite swapping algorithm at low temperature. Stoch. Process. Their Appl, 151:519–552, September 2022. doi:10.1016/j.spa.2022.06.015.

$\bullet $ Mark A. Peletier and André Schlichting. Cosh gradient systems and tilting. Nonlinear Anal., pages 113094, August 2022. doi:10.1016/j.na.2022.113094.

$\bullet $ Barbara Niethammer, Robert L. Pego, André Schlichting, and Juan J. L. Velázquez. Oscillations in a Becker-Döring model with injection and depletion. SIAM J. Appl. Math, 82(4):1194–1219, August 2022. doi:10.1137/20M1398664.

$\bullet $ Antonio Esposito, Rishabh S. Gvalani, André Schlichting, and Markus Schmidtchen. On a novel gradient flow structure for the aggregation equation. arXiv e-prints, December 2021. arXiv:2112.08317.

$\bullet $ André Schlichting and Christian Seis. The Scharfetter–Gummel scheme for aggregation–diffusion equations. IMA Journal of Numerical Analysis, May 2021. doi:10.1093/imanum/drab039.

$\bullet $ Constantin Eichenberg and André Schlichting. Self-similar behavior of the exchange-driven growth model with product kernel. Communications in Partial Differential Equations, 46(3):498–546, March 2021. doi:10.1080/03605302.2020.1845205.

$\bullet $ Antonio Esposito, Francesco S. Patacchini, André Schlichting, and Dejan Slepcev. Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit. Archive for Rational Mechanics and Analysis, 240(2):699–760, March 2021. doi:10.1007/s00205-021-01631-w.

$\bullet $ Rishabh S. Gvalani and André Schlichting. Barriers of the McKeanVlasov energy via a mountain pass theorem in the space of probability measures. J. Funct. Anal., 279(11):108720, December 2020. doi:10.1016/j.jfa.2020.108720.

$\bullet $ André Schlichting. The exchange-driven growth model: Basic properties and longtime behavior. J. Nonlinear Sci., 30(3):793–830, June 2020. doi:10.1007/s00332-019-09592-x.

$\bullet $ Matthias Erbar, Max Fathi, and André Schlichting. Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. Latin American Journal of Probability and Mathematical Statistics, 17(1):445, March 2020. doi:10.30757/alea.v17-18.

$\bullet $ José A. Carrillo, Rhishabh S. Gvalani, Grigorios. A. Pavliotis, and André Schlichting. Long-time behaviour and phase transitions for the MckeanVlasov equation on the torus. Arch. Ration. Mech. Anal., 235(1):635–690, January 2020. doi:10.1007/s00205-019-01430-4.

$\bullet $ André Schlichting and Martin Slowik. Poincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalities. Ann. Appl. Probab., 29(6):3438–3488, December 2019. doi:10.1214/19-AAP1484.

$\bullet $ André Schlichting. Macroscopic limit of the Becker–Döring equation via gradient flows. ESAIM Control Optim. Calc. Var., 25:22, July 2019. doi:10.1051/cocv/2018011.

$\bullet $ Joseph G. Conlon and André Schlichting. A non-local problem for the Fokker-Planck equation related to the Becker-Döring model. Discrete Contin. Dyn. Syst., 39(4):1821, April 2019. doi:10.3934/dcds.2019079.