DNA faculty working on PDEs

DNA faculty working on PDEs

Jørgen EndalJørgen Endal is interested in nonlinear equations of hyperbolic and parabolic type. Such equations include for example transport and diffusion terms. In particular, he is working on cases where the diffusion can be nonlocal. He has been treating fundamental questions like existence, uniqueness, and stability of such equations, but also finer properties like regularity and asymptotic behaviour.

Mats EhrnstromMats Ehrnstrom leads a research group investigating equations arising in fluid mechanics, in particular the Euler equations and nonlinear dispersive equations. Of particular interest here are travelling water waves, free-surface flows and rotational currents. A current focus is large-amplitude theory for nonlocal (Whitham-like) dispersive equations. The main interest of the group is on qualitative theory for PDEs, although research in numerical analysis is also pursued.

Katrin GrunertKatrin Grunert is working on nonlinear partial differential equations that describe wave phenomena. Of particular interest are nonlocal equations, like the Camassa-Holm equation or the Burgers Hilbert equation, which allow for wave breaking or shocks. Her research covers existence, uniqueness and stability results, as well as the local behavior of solutions.

Helge HoldenHelge Holden is working on several distinct classes of nonlinear partial differential equations that describe various wave phenomena. In particular, this includes hyperbolic conservation laws, the Camassa–Holm equation, and the nonlinear variational wave equation. In addition, Holden works on nonlinear stochastic partial differential equations as well as models related to traffic flow. Previously, he worked on flow in porous media and completely integrable systems.

Espen R. JakobsenEspen R. Jakobsen is working on nonlinear partial differential equations of parabolic or degenerate/mixed type: Hamilton-Jacobi/Isaacs, convection-diffusion, and porous media equations - along with fractional conservation laws and mean field games. He is known for his work on nonlocal models and approximations, involving functional and numerical analysis, probability and control theory. Recent directions include spatial statistics and stochastics. 

Theory of Partial Differential Equations right bar

The solution of the nonlinear variational wave equation. Figure.
The solution of the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0 in transformed variables. From the paper: H. Holden and X. Raynaud. Global Semigroup of Conservative Solutions of the Nonlinear Variational Wave Equation. Arch. Rational Mech. Anal. 201 (2011) 871–964.
Travelling waves with a linear vorticity distribution. Plot.
Travelling waves with a linear vorticity distribution. From the paper: Ehrnström, J. Escher, G. Villari. Steady water waves with multiple critical layers: interior dynamics. J. Math. Fluid Mech. 14(3) (2012) 407–419.