Helge Holden

Professor

Department of Mathematical Sciences

helge.holden@ntnu.no +47 73593514 +47 92038625

Sentralbygg 2, 1156, Gløshaugen, Alfred Getz vei 1

Activities:

I am the Principal Investigator of the research project ("Toppforsk") Waves and Nonlinear Phenomena (WaNP). I am the Secretary General of the International Mathematical Union (IMU). On the occasion of my 60th anniversary in 2016 the conference Non-linear PDEs, mathematical physics, and stochastic analysis was hosted here at NTNU. See proceedings Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis, European Mathematical Society Publishing House.

Research areas:

Differential equations, mathematical physics; in particular hyperbolic conservation laws and completely integrable systems. Stochastic analysis and flow in porous media.

Teaching:

Spring 2020: MA8105 Nonlinear PDEs and Sobolov Spaces

Fall 2021: TMA4305 Partial Differential Equations

Courses

Scientific, academic and artistic work

A selection of recent journal publications, artistic productions, books, including book and report excerpts. See all publications in the database

Journal publications

Grunert, Katrin; Holden, Helge. (2022) Uniqueness of conservative solutions for the Hunter–Saxton equation. Research in the Mathematical Sciences. vol. 9.
Holden, Helge; Karlsen, Kenneth Aksel Hvistendahl; Pang, Ho Cheung. (2022) Strong solutions of a stochastic differential equation with irregular random drift. Stochastic Processes and their Applications. vol. 150.
Coclite, Giuseppe Maria; Holden, Helge; Risebro, Nils Henrik. (2021) Singular diffusion with Neumann boundary conditions. Nonlinearity. vol. 34 (3).
Grunert, Katrin; Holden, Helge; Jakobsen, Espen Robstad; Stenseth, Nils Christian. (2021) Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model. Proceedings of the National Academy of Sciences of the United States of America. vol. 118 (4).
Holden, Helge; Karlsen, Kenneth Hvistendahl; Pang, Ho Cheung. (2021) The Hunter-Saxton equation with noise. Journal of Differential Equations. vol. 270.
Antonio Carrillo, José; Grunert, Katrin; Holden, Helge. (2020) A Lipschitz metric for the Camassa-Holm equation. Forum of Mathematics, Sigma. vol. 8 (e27).
Colombo, Rinaldo M; Holden, Helge; Marcellini, Francesca. (2020) On the microscopic modeling of vehicular traffic on general networks. SIAM Journal on Applied Mathematics. vol. 80 (3).
Antonio Carrillo, Jose; Grunert, Katrin; Holden, Helge. (2019) A Lipschitz metric for the Hunter–Saxton equation. Communications in Partial Differential Equations. vol. 44 (4).
Holden, Helge; Risebro, Nils Henrik. (2019) Models for dense multilane vehicular traffic. SIAM Journal on Mathematical Analysis. vol. 51 (5).
Hanche-Olsen, Harald; Holden, Helge; Malinnikova, Eugenia. (2018) An improvement of the Kolmogorov?Riesz compactness theorem. Expositiones mathematicae.
Holden, Helge; Risebro, Nils Henrik. (2018) Continuum limit of Follow-the-Leader models – a short proof. Discrete and Continuous Dynamical Systems. Series A. vol. 38 (2).
Holden, Helge; Risebro, Nils Henrik. (2018) Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Networks and Heterogeneous Media. vol. 13 (3).
Eckhardt, Jonathan; Gesztesy, Fritz; Holden, Helge; Kostenko, Aleksey; Teschl, Gerald. (2017) Real-Valued Algebro-Geometric Solutions of the Two-Component Camassa–Holm Hierarchy. Annales de l'Institut Fourier. vol. 67 (3).
Behrndt, Jussi; Gesztesy, Fritz; Holden, Helge; Nichols, Roger. (2016) Dirichlet-to-Neumann maps, abstract Weyl–Titchmarsh M-functions, and a generalized index of unbounded meromorphic operator-valued functions. Journal of Differential Equations. vol. 261 (6).
Colombo, Rinaldo M; Holden, Helge. (2016) Isentropic fluid dynamics in a curved pipe. Zeitschrift für Angewandte Mathematik und Physik. vol. 67 (5).
Colombo, Rinaldo; Holden, Helge. (2016) On the Braess Paradox with Nonlinear Dynamics and Control Theory. Journal of Optimization Theory and Applications. vol. 168 (1).
Dutta, Rajib; Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik. (2016) Convergence of finite difference schemes for the Benjamin–Ono equation. Numerische Mathematik. vol. 134 (2).
Gesztesy, Fritz; Holden, Helge; Nichols, Roger. (2016) Erratum to: On Factorizations of Analytic Operator-Valued Functions and Eigenvalue Multiplicity Questions. Integral equations and operator theory.
Grunert, Katrin; Holden, Helge. (2016) The general peakon-antipeakon solution for the Camassa-Holm equation. Journal of Hyperbolic Differential Equations. vol. 13 (2).
Hanche-Olsen, Harald; Holden, Helge. (2016) Addendum to “The Kolmogorov-Riesz compactness theorem” [Expo. Math. 28 (2010) 385–394]. Expositiones mathematicae. vol. 34.

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