# People

The project members are all part of the DNA *(Differential equations and Numerical Analysis)* group at the Department of Mathematical Sciences, NTNU.

### Principal Investigator

Helge 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 equations that model flow in porous media, e.g., flow of hydrocarbons in an oil reservoir, and equations that are completely integrable, e.g., the Korteweg–de Vries equation.

### Co-investigators

Mats Ehrnström 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 Grunert is interested in nonlinear partial differential equations that describe wave phenomena, in particular wave breaking, shock formations and stability results.

Espen R. Jakobsen is working on nonlinear partial differential equations and equations with nonlocal, fractional, or stochastic terms. His research portfolio includes different classes of models such as convection-diffusion, porous medium flow, control theory, stochastic analysis and finance. Typically these problems are degenerate and viscosity or entropy solutions are often involved. Key questions are uniqueness and stability/approximation of solutions.

Peter Lindqvist is interested in analysis. In particular he has devoted himself to non-linear elliptic and parabolic partial differential equations, often of a singular or degenerate type. Also so-called global equations with long range interaction are included. Viscosity solutions are involved. Regularity theory and boundary behaviour are central concepts.