Essays about: "Free-boundary problem"

Showing result 1 - 5 of 8 essays containing the words Free-boundary problem.

  1. 1. Symmetry in a free boundary problem

    University essay from KTH/Matematik (Avd.)

    Author : Seuri Basilio Kuosmanen; [2023]
    Keywords : Analysis of PDEs; Bernoulli-type boundary condition; free boundary problem; Laplacian operator; method of moving planes; symmetry; Analys av PDEs; Bernoulli-typ randvärde; frirandsproblem; Laplaceoperatorn; moving-plane metoden; symmetri;

    Abstract : We consider a variational formulation of a Bernoulli-type free boundary problem for the Laplacian operator with discontinuous boundary data. We show the existence of a weak solution to the problem. Moreover, we show that the solution has symmetry properties inherited by symmetric data. READ MORE

  3. 2. Gravity water waves over constant vorticity flows: from laminar flows to touching waves

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Francisco Gonçalves Jorge Dias de Carvalho; [2023]
    Keywords : Partial differential equations; Water waves; Euler equations; Free boundary problem; Bifurcation theory; Nonlinear functional analysis; Hilbert transform; Mathematics and Statistics;

    Abstract : In a recent paper, Hur and Wheeler proved the existence of periodic steady water waves over an infinitely deep, two-dimensional and constant vorticity flow and subject to gravity whose profile overhangs, among which, waves whose surface touches at a point, enclosing a bubble of air. We take this further, proving the existence of a continuous curve of water waves from a laminar flow up to a touching wave for fixed non-zero gravity. READ MORE

  4. 3. Pricing Financial Derivatives with the FiniteDifference Method

    University essay from KTH/Matematisk statistik

    Author : Sargon Danho; [2017]
    Keywords : American Call Option; Black-Scholes Equation; European Option; Finite Difference Method; Heat Equation; Optimal Exercise Boundary; Optimal Exit Boundary; Stock Loan; Amerikanska köpoptioner; Black-Scholes ekvation; europeiska optioner; finita differensmetoden; värmeledningsekvationen; optimala omvandlingsgräns; optimala avyttringsgräns; lån med aktier som säkerhet;

    Abstract : In this thesis, important theories in financial mathematics will be explained and derived. These theories will later be used to value financial derivatives. READ MORE

  5. 4. Convertible Bonds: a Qualitative and Numerical Analysis

    University essay from KTH/Matematik (Inst.)

    Author : Bianca Dufour Partanen; Emelie Järnberg; [2014]
    Keywords : ;

    Abstract : A convertible bond is a nancial instrument which has both an equity part and a xed-income part. The pricing of nancial securities has for quite obvious reasons become extensively studied in the past decades. In this paper we study the Black-Scholes model, based on the equity value, where the equity is modelled by geometric brownian motion. READ MORE

  6. 5. Pricing of American Options

    University essay from Lunds universitet/Matematisk statistik

    Author : Erik Andreasson; [2013]
    Keywords : Mathematics and Statistics;

    Abstract : This thesis investigates the free boundary value problem of pricing American put options written on one underlying asset. In particular, attention is given to nd an accurate approximation of the critical ex- ercise boundary. READ MORE