Browsing NTNU Open by Author "Ehrnstrøm, Mats"
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A Study of Dispersive Evolution Equations with Nonlocal Nonlinearities
Debech, Hager (Master thesis, 2015)In this thesis we consider a nonlinear-nonlocal equation of Whitham type. We prove the local well-posedness for our equation in the fractional Sobolev space by using the Picard Lindelöf existence theorem to prove the ... -
A Study of Rotational Water Waves using Bifurcation Theory
Aasen, Ailo (Master thesis, 2014)This thesis is concerned with the water wave problem. Using local bifurcation we establish small-amplitude steady and periodic solutions of the Euler equations with vorticity. Our approach is based on that of Ehrnström, ... -
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 ... -
Distributions, Schwartz Space and Fractional Sobolev Spaces
Gjestland, Fredrik Joachim (Master thesis, 2013)This thesis derives the theory of distributions, starting with test functions as a basis. Distributions and their derivatives will be analysed and exemplified. Schwartz functions are introduced, and the Fourier transform ... -
Existence of solitary-wave solutions to a class of pseudodifferential evolution equations
Haugå, Olav Willumsen (Master thesis, 2016)In this thesis, we present an original existence proof of solitary wave solutions to a class of pseudodifferential evolution equations. We seek traveling waves with constant velocity $c$ of the form $u(x-ct)$ of \begin{ ... -
On Steady Solutions of a Generalized Whitham Equation
Afram, Obed Opoku (Master thesis, 2017)We study the steady solutions of a generalized Whitham equation with the symbol m(x)=(tanh(x)\x)^s for 0 -
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 ... -
On the Well-Posedness of a Class of Whitham-like Nonlocal Equations with Weak Dispersion
Gjørtz, Henrik Fiskerstrand (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 ... -
Solitary waves for dispersive equations with inhomogeneous nonlinearities
Mæhlen, Ola Isaac Høgåsen (Master thesis, 2017)We prove existence of solitary-wave solutions to a class of pseudodifferential evolution equations with inhomogeneous nonlinearities in one spacial dimension, i.e. we prove existence of solutions of the form u(x-ct), where ... -
Water waves with compactly supported vorticity: A functional-analytic approach to bifurcation theory and the mathematical theory of traveling water waves
Varholm, Kristoffer (Master thesis, 2014)We study the mathematical theory of water waves. Local bifurcation theory is also discussed, including the Crandall-Rabinowitz theorem; an abstract theorem used to establish the presence of bifurcation points in the zero ...