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On the Stability of Solitary Water Waves with a Point Vortex
(Journal article; Peer reviewed, 2020)This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small‐amplitude waves with small enough vortex strength are ... -
On the structure and cohomology ring of connected Hopf algebras
(Peer reviewed; Journal article, 2019)Let p be a prime, and k be a field of characteristic p. We investigate the algebra structure and the structure of the cohomology ring for the connected Hopf algebras of dimension p3, which appear in the classification ... -
On the structure of certain C*-algebras arising from groups
(Doctoral Theses at NTNU, 1503-8181; 2013:159, Doctoral thesis, 2013) -
On the theory and numerical analysis of viscosity solutions
(Dr. ingeniøravhandling, 0809-103X; 2001:95, Doctoral thesis, 2001) -
On the Thin Film Muskat and the Thin Film Stokes Equations
(Journal article; Peer reviewed, 2019)The present paper is concerned with the analysis of two strongly coupled systems of degenerate parabolic partial differential equations arising in multiphase thin film flows. In particular, we consider the two-phase thin ... -
On the Three Ball Theorem for Solutions of the Helmholtz Equation
(Journal article, 2021)Let $u_k$ be a solution of the Helmholtz equation with the wave number $k$, $\Delta u_k+k^2 u_k=0$, on (a small ball in) either $\mathbb{R}^n$, $\mathbb{S}^n$, or $\mathbb{H}^n$. For a fixed point $p$, we define ... -
On the two-component Hunter–Saxton system
(Doctoral theses at NTNU;2017:146, Doctoral thesis, 2017)In 1991 Hunter and Saxton introduced a novel equation related to the dynamics of liquid crystals. The equation exhibited startling properties, among them wave breaking in finite time. Here we study the effects of ... -
On the two-phase fractional Stefan problem
(Journal article; Peer reviewed, 2020) -
On the uniqueness of eigenfunctions for the vectorial p-Laplacian
(Peer reviewed; Journal article, 2023)We study a nonlinear eigenvalue problem for vector-valued eigenfunctions and give a succinct uniqueness proof for minimizers of the associated Rayleigh quotient. -
On the Well-Posedness of a Class of Whitham-like Nonlocal Equations with Weak Dispersion
(Master thesis, 2015)We consider the Cauchy problems for a class of Whitham-like nonlocal equations with weak dispersion. Specifically, based on classical theory by Kato, local well-posedness in Sobolev spaces of order s>3/2 for this class of ... -
On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type
(Chapter, 2018)We study well-posedness and equivalence of different notions of solutions with finite energy for nonlocal porous medium type equations of the form ∂tu − Aϕ(u) = 0. These equations are possibly degenerate nonlinear diffusion ... -
On Tilting and Cluster-Tilting Theory: Algorithms and Mutations
(Doktoravhandlinger ved NTNU, 1503-8181; 2010:161, Doctoral thesis, 2010) -
On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
(Peer reviewed; Journal article, 2019)We consider the Whitham equation ut + 2uux + Lux = 0, where L is the nonlocal Fourier multiplier operator given by the symbol m(ξ) = p tanh ξ/ξ. G. B. Whitham conjectured that for this equation there would be a highest, ... -
On-Board Trend Analysis for Cargo Vessel Hull Monitoring Systems
(Peer reviewed; Journal article, 2022)With the increased focus on sustainability, de-carbonization and digitalization also the shipping industry is scrutinized. High steel weight implies high initial CO2 footprint but also higher operational CO2 footprint. ... -
An On-Campus Approach to Online Mathematics Teaching: A Case Study on a Pre-Calculus Course
(Peer reviewed; Journal article, 2022)Learning in STEM subjects is to a high degree based upon understanding logic, especially in subjects like mathematics. It has always been challenging to preserve the benefits of on-campus teaching and learning while ... -
One-sided Hölder regularity of global weak solutions of negative order dispersive equations
(Peer reviewed; Journal article, 2023)We prove global existence, uniqueness and stability of entropy solutions with initial data for a general family of negative order dispersive equations. These weak solutions are found to satisfy one-sided Hölder conditions ... -
A one-step Bayesian inversion framework for 3D reservoir characterization based on a Gaussian mixture model-A Norwegian Sea demonstration
(Peer reviewed; Journal article, 2021)We have developed a one-step approach for Bayesian prediction and uncertainty quantification of lithology/fluid classes, petrophysical properties, and elastic attributes conditional on prestack 3D seismic amplitude-varia ... -
Online interactive face-to-face learning in mathematics in engineering education
(Peer reviewed; Journal article, 2022)Online teaching has come to play an increasingly important role in higher education, especially during the Covid-19 pandemic. Being unable to be on campus with face-to-face teaching can be challenging. This article provides ... -
Online Learning in Vowpal Wabbit
(Master thesis, 2015)Online learning methods for sequentially arriving data are growing in popularity. Alternative batch learning methods scale poorly and have memory constraints. The scope of this thesis is to study online learning methods ... -
An operadic approach to substitution in Lie-Butcher series
(Peer reviewed; Journal article, 2022)The paper follows an operadic approach to provide a bialgebraic description of substitution for Lie–Butcher series. We first show how the well-known bialgebraic description for substitution in Butcher’s B-series can be ...