Fredrik Berntsson

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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)
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 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)
Let Ω be a bounded domain in R n with a Lipschitz boundary Γ divided into two parts Γ 0 and Γ 1 which do not intersect one another and have a common Lipschitz boundary. We consider the following Cauchy problem for the Helmholtz equation      ∆u + k 2 u = 0 in Ω, u = f on Γ 0 , ∂ ν u = g on Γ 0 , where k is the wave number, ∂ ν denotes the outward(More)