# Niclas Bernhoff

## Research

My research interests are mainly in kinetic theory and related topics. In particular, I mainly study the Boltzmann equation or Boltzmann-like equations. I have mainly studied these equations by considering discrete velocity models (DVMs), i.e. models where the velocity variable (or a corresponding variable) only takes a finite number of values, for them. It is a well-known fact that DVMs can approximate the Boltzmann equation up to any order. I have studied existence and uniqueness of boundary layers for DVMs of the Boltzmann equation for single species, binary mixtures (of two vapors or one vapor and one noncondensable gas), multicomponent mixtures, polyatomic molecules (with different internal energies), and chemical reactions, but also discrete versions of the quantum Boltzmann equation (Nordheim-Boltzmann or Uehling-Uhlenbeck equation) and an equation for excitations in a Bose gas interacting with a Bose condensate. I have also studied existence and uniqueness of shock profiles for DVMs of the Boltzmann equation for single species, mixtures, polyatomic molecules (with different internal energies), and chemical reactions.

Coming up:

7th International Workshop on Kinetic Theory and Applications June 19-21, 2017, Karlstad

## Bio

Niclas was born in 1971 in Lund. He got his B.Sc. (M.Sc.) in Mathematics at Uppsala University in 1995 (1998) and a diploma as Upper Secondary School Teacher in Mathematics from Stockholm Institute of Education in 1996.

In July 1996 he become a lecturer at Karlstad University, where he begun his PhD studies in 2000, presented his licentiate thesis "Discrete Velocity Models and Half-Space Problems" in 2003, and awarded his PhD in Mathematics in 2005. The title of his PhD thesis was "On Half-Space and Shock-Wave Problems for Discrete Velocity Models of the Boltzmann Equation". In 2005 he become promoted to senior lecturer/assistant professor, and in 2015 he become a Docent in Mathematics at Karlstad University (asssociate professor).

Niclas has been Guest Researcher at the Department of Mathematics at Parma University, Italy, (2 weeks May 2012, 1 week November 2013 - first visit supported by SVeFUM), at the Department of Mechanical Engineering and Science, Graduate School of Engineering at Kyoto University, Japan (1 month, October 2009, 2 weeks November 2015 - the visits were supported by the Japan Society for the Promotion of Science: No. PE 09549 and BR 150501), at the Department of Mathematics at Bordeaux University (1 week September 2016, 1 week October 2017 -supported by French Institute in Sweden in 2016 and by SVeFUM in 2017), Department of Mathematics at Ecole Polytechnique, Paris (1 week September 2016, 1 week October 2017, visiting also Paris Diderot University, and (in 2016) also Paris Dauphine University - supported by French Institute in Sweden in 2016 and by SVeFUM in 2017)) and during October 2017, 1 week in Hong Kong (at Chinese University of Hong Kong and City University of Hong Kong).

He was (together with Bernt Wennberg, Chalmers University of Technology) the main organizer of the "6th International Workshop on Kinetic Theory & Applications" at Karlstad University in May 12-14, 2014, and gave himself several talks in international conferences.

He also participated in teacher exchanges inside the Erasmus/Erasmus+ Programmes at the Department of Mathematics at Lucian Blaga, University of Sibiu (3 weeks May 2009, 2 weeks May 2010, 2 weeks May 2011, 2 weeks April-May 2013, 1 week March 2016, 1 week May-June 2017 - planned), and Department of Mathematics at University of Catania (1 week October 2014).

## Related info

Conferences recent/coming up:

Workshop on Kinetic and Related models, October 25-26, 2017, Hong Kong

7th International Workshop on Kinetic Theory and Applications, June 19-21, 2017, Karlstad

Recent Advances on Particle Systems in Kinetic Theory, May 8-12, 2017, Austin, Texas

## Selected publications

N. Bernhoff, Boundary layers for discrete kinetic models: multicomponent mixtures, polyatomic molecules, bimolecular chemical reactions, and quantum kinetic equations, Kinet. Relat. Models, 10, 2017, p.925-955.

N. Bernhoff, Discrete velocity models for multicomponent mixtures and polyatomic molecules without nonphysical collision invariants and shock profiles, AIP Conf. Proc. 1786, 2016, p.040005-1-8.

N. Bernhoff and M. Vinerean, Discrete velocity models for mixtures without nonphysical collision invariants, J. Stat. Phys., 165, 2016, p.434-453.

N. Bernhoff, Half-space problem for the discrete Boltzmann equation: condensing vapor flow in the presence of a non-condensable gas, J. Stat. Phys., 147, 2012, p. 1156-1181.

N. Bernhoff and A.V. Bobylev, Weak shock waves for the general discrete velocity model of the Boltzmann equation, Comm. Math. Sci., 5, 2007, p. 815-832

A.V. Bobylev and N. Bernhoff, Discrete velocity models and dynamical systems, in Lecture Notes on the Discretization of the Boltzmann Equation, N.Bellomo and R.Gatignol, eds., World Scientific Publishing Co, 2003, p. 203-222

( see also publications)

## Publications

- Niclas Bernhoff, 2017
- Niclas Bernhoff, 2016
- Niclas Bernhoff, Mirela Vinerean Bernhoff, 2016
- Niclas Bernhoff, 2016
- Niclas Bernhoff, 2015
- Niclas Bernhoff, 2012
- Niclas Bernhoff, 2012
- Niclas Bernhoff, 2012
- Niclas Bernhoff, 2010
- Niclas Bernhoff, 2010
- Niclas Bernhoff, 2008
- Niclas Bernhoff, Alexander Bobylev, 2007
- Niclas Bernhoff, Alexander Bobylev, 2007
- Niclas Bernhoff, 2005
- Alexander Bobylev, Niclas Bernhoff, 2003
- Niclas Bernhoff, 2003