Helge Holden
Background and activities
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
- MA8103 - Non-Linear Hyperbolic Conservation Laws
- TMA4305 - Partial Differential Equations
- MA8105 - Non-Linear Partial Differential Equations and Sobolev Spaces
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
- (2021) Singular diffusion with Neumann boundary conditions. Nonlinearity. vol. 34 (3).
- (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).
- (2021) The Hunter-Saxton equation with noise. Journal of Differential Equations. vol. 270.
- (2021) Singular diffusion with Neumann boundary conditions. Nonlinearity. vol. 34 (3).
- (2020) A Lipschitz metric for the Camassa-Holm equation. Forum of Mathematics, Sigma. vol. 8 (e27).
- (2020) On the microscopic modeling of vehicular traffic on general networks. SIAM Journal on Applied Mathematics. vol. 80 (3).
- (2019) A Lipschitz metric for the Hunter–Saxton equation. Communications in Partial Differential Equations. vol. 44 (4).
- (2019) Models for dense multilane vehicular traffic. SIAM Journal on Mathematical Analysis. vol. 51 (5).
- (2018) An improvement of the Kolmogorov?Riesz compactness theorem. Expositiones mathematicae.
- (2018) Continuum limit of Follow-the-Leader models – a short proof. Discrete and Continuous Dynamical Systems. Series A. vol. 38 (2).
- (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).
- (2017) Real-Valued Algebro-Geometric Solutions of the Two-Component Camassa–Holm Hierarchy. Annales de l'Institut Fourier. vol. 67 (3).
- (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).
- (2016) Isentropic fluid dynamics in a curved pipe. Zeitschrift für Angewandte Mathematik und Physik. vol. 67 (5).
- (2016) On the Braess Paradox with Nonlinear Dynamics and Control Theory. Journal of Optimization Theory and Applications. vol. 168 (1).
- (2016) Convergence of finite difference schemes for the Benjamin–Ono equation. Numerische Mathematik. vol. 134 (2).
- (2016) Erratum to: On Factorizations of Analytic Operator-Valued Functions and Eigenvalue Multiplicity Questions. Integral equations and operator theory.
- (2016) The general peakon-antipeakon solution for the Camassa-Holm equation. Journal of Hyperbolic Differential Equations. vol. 13 (2).
- (2016) Addendum to “The Kolmogorov-Riesz compactness theorem” [Expo. Math. 28 (2010) 385–394]. Expositiones mathematicae. vol. 34.
- (2016) Burgers meets Braess. Oberwolfach Reports. vol. 13 (2).