Blar i NTNU Open på forfatter "Arnesen, Mathias Nikolai"
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A non-local approach to waves of maximal height for the Degasperis-Procesi equation
Arnesen, Mathias Nikolai (Journal article; Peer reviewed, 2019)We consider the non-local formulation of the Degasperis-Procesi equation , where L is the non-local Fourier multiplier operator with symbol . We show that all , pointwise travelling-wave solutions are bounded above by the ... -
An Introduction to Distributions and Sobolev Spaces, and a Study of the Fractional Partial Differential Operator1+ (-Δ)s⁄2
Arnesen, Mathias Nikolai (Master thesis, 2013)In this thesis we derive the basic theory for distributions, fractional and classical Sobolevspaces and the direct method of variations, and apply this theory to discuss solutions of the dirichlet problem for a fractional ... -
Non-uniform dependence on initial data for equations of Whitham type
Arnesen, Mathias Nikolai (Journal article, 2019)We consider the Cauchy problem ∂tu + u∂xu + L(∂xu) = 0, u(0, x) = u0(x) for a class of Fourier multiplier operators L, and prove that the solution map u0 7→ u(t) is not uniformly continuous in Hs on the real line or on the ... -
On nonlocal dispersive equations and water waves
Arnesen, Mathias Nikolai (Doctoral theses at NTNU;2018:84, Doctoral thesis, 2018) -
On the Existence of Periodic Traveling Waves to the Whitham Equation
Hildrum, Fredrik (Master thesis, 2015)We study the existence of periodic traveling waves to the Whitham equation, which is a nonlinear, nonlocal and dispersive differential equation proposed by Whitham as a model for surface gravity waves featuring the exact ...