Bengt Ove Turesson

Linköping University | LiU · Department of Mathematics (MAI)

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The Cauchy problem for the Helmholtz equation is considered. It was demonstrated in a previous paper by the authors that the alternating algorithm suggested by V.A. Kozlov and V.G. Maz’ya does not converge for large wavenumbers k in the Helmholtz equation. Here, we present some simple modifications of the algorithm which may restore the convergence...

The Cauchy problem for the Helmholtz equation appears in various applications. The problem is severely ill-posed and regularization is needed to obtain accurate solutions. We start from a formulation of this problem as an operator equation on the boundary of the domain and consider the equation in spaces. By introducing an artificial boundary in th...

We study the impact of age-structure and temporal environmental variability on the persistence of populations. We use a linear age-structured model with time-dependent vital rates. It is the same as the one presented by Chipot in (Arch. Ration. Mech. Anal. 82(1):13-25, 1983), but the assumptions on the vital rates are slightly different. Our main i...

The Cauchy problem for the Helmholtz equation is considered. It was demonstrated in a previous paper by the authors that the alternating algorithm suggested by V.A. Kozlov and V.G. Maz'ya does not converge for large wavenumbers k in the Helmholtz equation. Here we present some simple modifications of the algorithm which may restore the convergence....

In this paper we study the Cauchy problem for the Helmholtz equation. This problem appears in various applications and is severely ill-posed. The modified alternating procedure has been proposed by the authors for solving this problem but the convergence has been rather slow. We demonstrate how to instead use conjugate gradient methods for accelera...

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. T...

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 shap...

This paper considers to the equation [\int_{S} \frac{U(Q)}{|P-Q|^{N-1}} dS(Q) = F(P), P \in S,] where the surface S is the graph of a Lipschitz function \phi on R^N, which has a small Lipschitz constant. The integral in the left-hand side is the single layer potential corresponding to the Laplacian in R^{N+1}. Let \Lambda(r) be a Lipschitz constant...

When charged particles are placed on an uncharged metallic body, the charged particles redistribute themselves along the surface of the body until they reach a point or a configuration that no net tangential force is experienced on each particle. That point is referred to as electrostatic equilibrium configuration or simply as static equilibrium co...

For a locally convex space with the topology given by a family {p(┬; α)} α ∈ ω of seminorms, we study the existence and uniqueness of fixed points for a mapping defined on some set . We require that there exists a linear and positive operatorK, acting on functions defined on the index set Ω, such that for everyu, Under some additional assumptions,...

We consider the following equation for the Riesz potential of order one: Uniqueness is proved in the class of solutions for which the integral is absolutely convergent for almost every x. We also prove an existence result and derive an asymptotic formula for solutions near the origin. Our analysis is carried out in local L p -spaces and Sobolev spa...

We consider the problem of reconstruction of the temperature from measurements of the temperature and heat flux on a part of the boundary and present iterative methods for solving this problem. The characteristic feature of the methods is the fact that in each iteration step, well-posed problems for the same equation are solved. The regularizing ch...

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