Dr. Jan Friedrich

Academic Positions

• Principal Investigator, SPP 2410: CoScaRa, DFG, (Sep 2023 - present)
  Project: Balance laws with space-dependent nonlocalities: modeling, simulation and uncertainty quantification (NonLoc)
• PostDoc, IGPM, RWTH Aachen University (Jan 2022 - present)
  Research group of Prof. Dr. Michael Herty
• PostDoc, WIM, Mannheim University (Sep - Dec 2021)
  Research group of Prof. Dr. Simone Göttlich
• PhD in Mathematics,WIM, Mannheim University (Sep 2017 - Aug 2021)
  Supervisor: Prof. Dr. Simone Göttlich

Research Interests

• Nonlocal Conservation Laws and its Applications
• Mathematical Modeling of Vehicular Traffic
• Mathematical and Numerical Analysis of PDEs
• (High-order) Numerical Schemes for PDEs
• PDE-constrained Optimization
• Lyapunov Stabilization of PDEs
• Particle-based Optimization Methods

Projects

• Balance laws with space-dependent nonlocalities: modeling, simulation and uncertainty quantification (NonLoc)
  DFG-SPP 2410: CoScaRa, 2024 - 2027

• Design and development of numerical scheme for nonlocal conservation laws in multi-dimension
  Paired Early Career Fellowship in Applied Research (PECFAR), Indo-German Science & Technology Centre (IGSTC, BMBF),
  together with Dr. Samala Rathan, 2025

Publications

Preprints

• J. Friedrich, S. Schraven, F. Kiessling, M. Herty,
  Source Identification by Consensus-Based Optimization
  2024.

Peer-Reviewed Journal Articles

• F. Chiarello, J. Friedrich, S. Göttlich,
  A non-local traffic flow model for 1-to-1 junctions with buffer
  Netw. Heterog. Media, 19(1):405-429, 2024.

• J. Friedrich, S. Göttlich, A. Keimer, L. Pflug,
  Conservation laws with nonlocal velocity - the singular limit problem
  SIAM J. Appl. Math., 84(2):497-522, 2024.

• J. Friedrich, S. Göttlich, M. Herty,
  Lyapunov stabilization for nonlocal traffic flow models
  SIAM J. Control Optim., 61(5):2849-2875 , 2023.

• J. Friedrich, S. Sudha, S. Rathan,
  Numerical schemes for a class of nonlocal conservation laws: a general approach
  Netw. Heterog. Media, 18(3): 1335-1354 , 2023.

• J. Friedrich, S. Göttlich, A. Uphoff
  Conservation laws with discontinuous flux function on networks: a splitting algorithm
  Netw. Heterog. Media, 18(1): 1-28 , 2023.

• A. Bayen, J. Friedrich, A. Keimer, L. Pflug, T. Veeravalli
  Modeling Multilane Traffic with Moving Obstacles by Nonlocal Balance Laws
  SIAM J. Appl. Dyn. Syst., 21 (2),1495--1538, 2022.

• J. Friedrich, S. Göttlich, M. Osztfalk
  Network models for nonlocal traffic flow
  ESAIM Math. Model. Numer. Anal., 56, 213--235, 2022.

• J. Friedrich, E. Rossi, S. Göttlich
  Nonlocal approaches for multilane traffic models
  Commun. Math. Sci., 19, 2291--2317, 2021.

• F. Chiarello, J. Friedrich, P. Goatin, S. Göttlich
  Micro-Macro limit of a non-local generalized Aw-Rascle type model
  SIAM J. Appl. Math., 80, 1841–1861, 2020.

• F. Chiarello, J. Friedrich, P. Goatin, S. Göttlich, O. Kolb
  A non-local traffic flow model for 1-to-1 junctions
  European J. Appl. Math., 31, 1029-1049, 2020.

• J. Friedrich, O. Kolb
  Maximum principle satisfying CWENO schemes for nonlocal conservation laws
  SIAM J. Sci. Comput., 41, A973-A988, 2019.

• J. Friedrich, O. Kolb, S. Göttlich
  A Godunov type scheme for a class of LWR traffic flow models with non-local flux
  Netw.Heterog. Media, 13, pp. 531-547, 2018.

Peer-Reviewed Conference Proceedings

• J. Friedrich, S. Göttlich, A. Keimer, L. Pflug,
  Conservation laws with nonlocality in density and velocity and their applicability in traffic flow modelling
  Hyperbolic Problems: Theory, Numerics, Applications. Volume II, 2024.

• J. Friedrich
  Lyapunov stabilization of a nonlocal LWR model
  PAMM, Proceedings in Applied Mathematics and Mechanics, 2023.

PhD Thesis

• J. Friedrich
  Traffic flow models with nonlocal velocity
  ISBN 978-3-8439-4903-3, 2021.
  PDF-file

Other

• J. Friedrich
  Autonome Autos: Kein Fahrer, kein Stau?
  KlarText Blog, 2023.

Research Stays

• Indian Institute of Petroleum and Energy (IIPE), Visakhapatnam, India, Feb.-Mar. 2024, financially supported by IIPE
• Arizona State University (ASU), Phoenix, USA, Aug. 2019, financially supported by DAAD-PPP USA
• INRIA, Sophia Antipolis, France, July and Nov. 2019, financially supported by DAAD France and PHC Procope
• INRIA, Sophia Antipolis, France, Jan. 2019, Research Tandem, financially supported by DAAD within the IPID4all program

Teaching Experience

Lectures

Mar. '24	Applications of scalar hyperbolic conservation laws,	PhD-Course,	Indian Institute of Petroleum and Energy
[WT23]	Applications of scalar conservation laws,	Master (+exercise class),	RWTH Aachen University
[WT21]	Numerical Methods for Ordinary Differential Equations,	Master,	University of Mannheim

Teaching Assistant (Excerpt)

[WT24, WT23, WT22]	Mathematics 1 for civil engineers,	Bachelor-Course,	RWTH Aachen University
[ST24, ST23,ST22]	Mathematics 2 for civil engineers,	Bachelor-Course,	RWTH Aachen University
[WT21]	Numerical Methods for Ordinary Differential Equations,	Master-Course,	University of Mannheim
[ST21, ST20, ST19]	Numerical Methods for Partial Differential Equations,	Master-Course	University of Mannheim
[WT20, WT19]	Applications of Scalar Conservation Laws,	Master-Course,	University of Mannheim
[WT20, WT19, ST18]	Numerics,	Bachelor-Course,	University of Mannheim

Conferences and Workshops

Upcoming Conferences

• Numerical Aspects of Hyperbolic Balance Laws and Related Problems, Nonlocal balance laws: Numerical schemes and applications to traffic flow, Invited Speaker, Ferrara, Italy, Dec. 2024



As Organizer

• Recent Trends in Optimization and Control: Follow-up Workshop, Organizing & Scientific Committee, Dakar, Senegal, Oct. 2024
• Recent Trends in Optimization and Control: Short course and Workshop, Organizing & Scientific Committee, Pertoria, South Africa, Sep. 2023
• SIAM PD 2022, Co-Chair, Minisymposium: Nonlocal conservation laws, virtual, March 2022
• DMV-ÖMG Annual Conference 2021, Co-Chair, Minisymposium 13: Nonlocal conservation laws, virtual, Sep. 2021
• 13th International Conference on Monte Carlo Methods and Applications, Local Organizer, virtual, Aug. 2021



Most Recent Talks (Excerpt)

• Workshop 'Control and Optimization in the Age of Data', Source identification via a consensus-based optimization algorithm using different moment hierarchies, Bayreuth, Sep. 2024
• Nonlocal Modelling in Fluidmechanical Applications, Numerical schemes for conservation laws with space-dependent nonlocalities , Invited Speaker, Mannheim, Sep. 2024
• HYP 2024, Lyapunov Stabilization for Nonlocal Traffic Flow Models, Contributed Talk, Shanghai, China, Jul. 2024
• Recent Trends in Optimization and Control: Short course and Workshop, Cell tracking for the radiative transfer equation, Plenary Talk, Pertoria, South Africa, Sep. 2023
• 16th Hirschegg Workshop on Conservation Laws, Traffic flow models with nonlocal velocity: The singular limit problem, Hirschegg, Austria, Sep. 2023

Other

Guest Editor

• Special Issue:
  Nonlocal Conservation laws
  Networks and Heterogeneous Media




Reviewer for

• Bulletin of the Brazilian Mathematical Society
• Computers and Chemical Engineering
• Discrete and Continuous Dynamical Systems. Series B.
• ESAIM Math. Model. Numer. Anal.
• IMA Journal of Numerical Analysis
• Kinetic and Related Models
• Mathematical Biosciences and Engineering
• Mathematics and Computers in Simulation
• Networks and Heterogeneous Media
• SIAM Journal on Applied Dynamical Systems
• SIAM Journal on Applied Mathematics
• Zeitschrift für Angewandte Mathematik und Physik