Waves and Nonlinear Phenomena

(by Helge Holden, Professor at NTNU)

The Department of Mathematical Sciences at NTNU was happy to receive in 2016 one of the “Toppforsk” (Excellence) grants from the Research Council of Norway. Fiercely competitive, these grants are given to smaller groups across all sciences for a period of 5 years. The grant – Waves and Nonlinear Phenomena (WaNP) –  amounts to NOK 25 mill., and participants are H. Holden (PI) and M. Ehrnström, U. S. Fjordholm, K. Grunert, E. Jakobsen and P. Lindqvist.  The project will support 4 PhD students as well as 2 Postdoctoral Fellows.

The purpose of WaNP is to analyze the interplay of singularities and nonlocal effects in the solution of  carefully selected partial differential equations that model wave phenomena. Wave motion is ubiquitous, from the familiar waves in fluids to internal waves in solids. The key question is try to increase our understanding of how nonlocalities affect the appearance of singularities in wave equations.  A deeper understanding of these fundamental questions will also enhance our insight for more complex questions.

In the project several  familiar equations will be studied, including Camassa–Holm type equations, Burgers–Hilbert and Burgers–Poisson equations, Whitham equation, as well as degenerate parabolic convection-diffusion equations. But also novel equations that are nonlocal integro-differentia equations, often coming from applications will be analyzed. In addition, one will study partial differential equations with uncertainties, including equations with uncertain initial data.

For more information see the project webpage.

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Helge Holden holds a PhD from the University of Oslo from 1985, and has a been a professor at the Norwegian University of Science and Technology since 1991.
He was President of ECMI in 2004–2006, and Secretary and Vice President of the European Mathematical Society in 2003–2006 and 2007–10, respectively.  Since
2015 Holden has been the Secretary of the International Mathematical Union.

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