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We consider an inverse heat conduction problem, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line… (More)

We present a modification of the alternating iterative method, which was introduced by Kozlov and Maz'ya, for solving the Cauchy problem for the Helmholtz equation in a Lipschitz domain. The reason for this modification is that the standard alternating iterative algorithm does not always converge for the Cauchy problem for the Helmholtz equation. The method… (More)

We consider an inverse heat conduction problem, the Sideways Heat Equation , which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. We illustrate this in Figure 0.1. Mathematically it can be formulated as a Cauchy problem for the heat equation in the… (More)

- Emanuel Evarest, Fredrik Berntsson, Martin Singull, Wilson Charles
- 2016

Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a… (More)

In this paper we present a one-dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers. The model involves two variables: the radial displacement of the vessel's wall and the pressure, and consists of two coupled equations of parabolic and hyperbolic type. Numerical simulations on a straight segment… (More)

With this thesis we aim to create an efficient scheduling algorithm for elevators that can move in multiple directions and establish if and when the algorithm is efficient in comparison to algorithms constructed for traditional elevator algorithms. To measure efficiency, a simulator is constructed to simulate an elevator system implementing different… (More)

In this paper, we introduce the concept of parameter identification problems , which are inverse problems, as a methodology to inpainting. More specifically, as a first study in this new direction, we generalize the method of harmonic inpainting by studying an elliptic equation in divergence form where we assume that the diffusion coefficient is unknown. As… (More)

- Fredrik Berntsson, Vladimir A Kozlov, Lydie Mpinganzima, Bengt Ove Turesson
- 2014

The Cauchy problem for the Helmholtz equation appears in applications related to acoustic or electromagnetic wave phenomena. The problem is ill–posed in the sense that the solution does not depend on the data in a stable way. In this paper we give a detailed study of the problem. Specifically we investigate how the ill–posedness depends on the shape of the… (More)