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Eenhoorn, Jasper (author)The (nonlinear) behaviour of laser beams can be described with Nonlinear Schrödinger equations (NLS). The purpose of this thesis is to shed light on two mathematical papers that give existence and uniqueness results for an NLS equation called the soliton equation. The contribution is to expand the level of detail with which the analysis and some...bachelor thesis 2023
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van Winden, Joris (author)In this thesis we consider orbital stability of certain patterns in stochastic partial differential equations. We study two examples: a rotating wave in a twodimensional reactiondiffusion equation and a soliton in a parametrically forced nonlinear Schrödinger equation. In both cases, we show that, for small noise, solutions to the stochastic...master thesis 2022
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Roodenburg, Floris (author)In this thesis we consider the incompressible and stationary Stokes problem with Navierslip boundary conditions on an infinite twodimensional wedge with opening angle θ. As is common for differential equations on domains with corners, the problem is decomposed into a singular expansion near the corner (polynomial problem) and a regular...master thesis 2022
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Wisse, Anouk (author)This thesis treats the thinfilm equation which models the film height $h$ for a viscous film in the complete wetting regime. We show existence and uniqueness to the thinfilm equation with mobility m(h) = h<sup>n</sup> and mobility exponent n∈ (1,3/2)∪ (3/2,3). The thinfilm equation is rewritten as an abstract Cauchy problem and usage of semi...master thesis 2022
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van Noord, Zomer (author)This thesis considers solutions to the discrete Nagumo equation u˙ n = d(un−1 − 2un + un+1) + f(un), n ∈ Z. For sufficiently large d, the solutions are of the form un(t) = U(n + ct) with c > 0. This thesis contains the proof of existence of traveling wave solutions of the discrete Nagumo equations and originates from...bachelor thesis 2022
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Westdorp, Rik (author)In this thesis, a variation on the nonlinear Schrödinger (NLS) equation with multiplicative noise is studied. In particular, we consider a stochastic version of the parametricallyforced nonlinear Schrödinger equation (PFNLS), which models the effect of linear loss and the compensation thereof by phasesensitive amplification in pulse...master thesis 2021
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Hoogendijk, Jochem (author)This master's thesis introduces a new $p$dependent coercivity condition through which $L^p(\Omega; L^2([0, T]; X))$ estimates can be obtained for a large class of SPDEs in the variational framework. Using these estimates, we obtain existence and uniqueness results by using a Galerkin approximation argument. The framework that is built is...master thesis 2021
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Vural, Asya (author)The porous medium equation $\dv{t}u=\dv{x}(k(u)\dv{x}u)$ is a nonlinear degenerate parabolic partial differential equation. Consequently, existence and uniqueness of its solutions is not immediately evident.<br/>This bachelor thesis presents a detailed discussion of Atkinson's and Peletier's 1971 article ``Similarity profiles of flows through...bachelor thesis 2021
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Wisse, A.C. (author)This thesis considers the thinfilm equation in partial wetting. The mobility in this equation is given by h<sup>3</sup>+λ<sup>3n</sup>h<sup>n</sup>, where h is the film height, λ is the slip length and n is the mobility exponent. The partial wetting regime implies the boundary condition dh/dz>0 at the triple junction....bachelor thesis 2020