Niklas L. P. Lundström

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• PhD
• Professor (Associate) at Umeå University

In this paper, we derive simple analytical bounds for solutions of $x - \ln x = y -\ln y$ , and use them for estimating trajectories following Lotka–Volterra-type integrals. We show how our results give estimates for the Lambert W function as well as for trajectories of general predator–prey systems, including, for example, Rosenzweig–MacArthur equ...

In this paper, we present a telegraph diffusion model with variable exponents for image despeckling. Moving beyond the traditional assumption of a constant exponent in the telegraph diffusion framework, we explore three distinct variable exponents for edge detection. All of these depend on the gray level of the image or its gradient. We rigorously...

In this note we derive simple analytical approximations for the solutions of x − log x = y − log y and use them for estimating trajectories following Lotka-Volterra-type integrals. We show how our results imply estimates for the Lambert W function as well as for trajectories of general predator-prey systems, including e.g. Rosenzweig McArthur equat...

The local pivotal method (LPM) is a successful sampling method for taking well-spread samples from discrete populations. We show how the LPM can be utilized to sample from arbitrary continuous distributions and thereby give powerful variance reduction in general cases. The method creates an "automatic stratification" on any continuous distribution,...

We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear nonhomogeneous degenerate elliptic equations on the form $$ F(x,u,Du,D^{2}u) = 0 $$ under suitable assumptions allowing for non-Lipschitz growth in the gradient term. In case of smooth boundaries, we also prove a Hopf lemma, a boundary Harnack inequ...

The mathematical theory for optimal switching is by now relatively well developed, but the number of concrete applications of this theoretical framework remains few. In this paper, we bridge parts of this gap by applying optimal switching theory to a conceptual production planning problem related to hydropower. In particular, we study two examples...

We prove the existence of a unique viscosity solution to certain systems of fully nonlinear parabolic partial differential equations with interconnected obstacles in the setting of Neumann boundary conditions. The method of proof builds on the classical viscosity solution technique adapted to the setting of interconnected obstacles and construction...

We characterize lower growth estimates for subsolutions in halfspaces of fully nonlinear partial differential equations on the formF(x,u,Du,D2u)=0 in terms of solutions to ordinary differential equations built upon assumptions on F. Using this characterization we derive several sharp Phragmen–Lindelöf-type theorems for certain classes of well known...

Suppose that p ∈ (1, ∞], v ∈ [1/2, ∞) and S v = (x, y) ∈ R 2 \ {(0, 0)}; |φ| < π 2v , where φ is the polar angle of (x, y). Let R > 0 and ω p (x) be the p-harmonic measure of ∂B(0, R) ∩ S v at x with respect to B(0, R) ∩ S v. We prove that there exists a constant C such that C −1 |x| R k(v,p) ≤ ω p (x) ≤ C |x| R k(v,p) where the exponent k(v, p) is...

We prove the existence of a unique viscosity solution to certain systems of fully nonlinear parabolic partial differential equations with interconnected obstacles in the setting of Neumann boundary conditions. The method of proof builds on the classical viscosity solution technique adapted to the setting of interconnected obstacles and construction...

We characterize lower growth estimates for subsolutions in halfspaces of fully nonlinear partial differential equations on the form F (x, u, Du, D 2 u) = 0 in terms of solutions to ordinary differential equations built solely upon a growth assumption on F. Using this characterization we derive several sharp Phragmen-Lindelöf-type theorems for certa...

The mathematical theory for optimal switching is by now relatively well developed, but the number of concrete applications of this theoretical framework remains few. In this paper, we bridge parts of this gap by applying optimal switching theory to a set of production planning problems related to hydropower plants. In particular, we study two diffe...

Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena can not be trace...

In this article, we consider the setting of single-valued, smoothly varying directions of reflection and non-smooth time-dependent domains whose boundary is H\"{o}lder continuous in time. In this setting, we prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection. In the same setting, we also...

Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as pretty good yield (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservat...

We study viscosity solutions to a system of nonlinear degenerate parabolic partial integro-differential equations with interconnected obstacles. This type of problem occurs in the context of optimal switching problems when the dynamics of the underlying state variable is described by an n-dimensional Lévy process. We first establish a continuous de...

We study viscosity solutions to a system of nonlinear degenerate parabolic partial integro-differential equations with interconnected obstacles. This type of problem occurs in the context of optimal switching problems when the dynamics of the underlying state variable is described by an $n$-dimensional Levy process. We first establish a continuous...

Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena can not be trace...

We consider a Rosenzweig–MacArthur predator-prey system which incorporateslogisticgrowthofthepreyintheabsenceofpredatorsandaHollingtypeIIfunctionalresponsefor interaction between predators and preys. We assume that parameters take values in a range which guarantees that all solutions tend to a unique limit cycle and prove estimates for the maximal...

We consider a Rosenzweig-MacArthur predator-prey system which incorporates logistic growth of the prey in the absence of predators and a Holling type II functional response for interaction between predators and preys. We assume that parameters take values in a range which guarantees that all solutions tend to a unique limit cycle and prove estimate...

Sustainable yields that are at least $80\%$ of the maximum sustainable yield are sometimes referred to as pretty good yield (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conser...

Biological pest control is increasingly used in agriculture as a an alternative to traditional chemical pest control. In many cases, this involves a one-off or periodic release of naturally occurring and/or genetically modified enemies such as predators, parasitoids, or pathogens. As the interaction between these enemies and the pest is complex and t...

Biological pest control is increasingly used in agriculture as a an alternative to traditional chemical pest control. In many cases, this involves a one-off or periodic release of naturally occurring and/or genetically modified enemies such as predators, parasitoids, or pathogens. As the interaction between these enemies and the pest is complex and...

We prove estimates of a $p$-harmonic measure, $p \in (n-m, \infty]$, for sets in $\mathbf{R}^n$ which are close to an $m$-dimensional hyperplane $\Lambda \subset \mathbf{R}^n$, $m \in [0,n-1]$. Using these estimates, we derive results of Phragm\'en-Lindel\"of type in unbounded domains $\Omega \subset \mathbf{R}^n\setminus \Lambda$ for $p$-subharmon...

Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depe...

We investigate various boundary decay estimates for $p(\cdot)$-harmonic functions. For domains in $\mathbb{R}^n, n\geq 2$ satisfying the ball condition ($C^{1,1}$-domains) we show the boundary Harnack inequality for $p(\cdot)$-harmonic functions under the assumption that the variable exponent $p$ is a bounded Lipschitz function. The proof involves...

In this paper we study viscosity solutions to the system (formula present) is a non-local integro-partial differential operator. A special case of this type of system of variational inequalities with terminal data occurs in the context of optimal switching problems when the dynamics of the underlying state variables is described by an N-dimensional...

We prove that combinations of small eccentricity, ovality and/or triangularity in the rotor and stator can produce complex whirling motions of an unbalanced rotor in large synchronous generators. It is concluded which structures of shape deviations that are more harmful, in the sense of producing complex whirling motions, than others. For each such...

In this paper we study the system $$\begin{aligned}&\min \biggl \{-\mathcal H u_i(x,t)-\psi _i(x,t),u_i(x,t)-\max _{j\ne i}(-c_{i,j}(x,t)+u_j(x,t))\biggr \}=0,\\&u_i(x,T)=g_i(x),\ i\in \{1,\ldots ,d\}, \end{aligned}$$ where $(x,t)\in \mathbb R ^{N}\times [0,T]$ . A special case of this type of system of variational inequalities with terminal da...

When sampling from a finite population there is often auxiliary information available on unit level. Such information can be used to improve the estimation of the target parameter. We show that probability samples that are well spread in the auxiliary space are balanced, or approximately balanced, on the auxiliary variables. A consequence of this b...

We study the asymptotic behaviour of a p-harmonic measure w(p), p is an element of (1, infinity], in a domain Omega subset of R-2, subject to certain regularity constraints. Our main result is that w(p) (B (w, delta) boolean AND partial derivative Omega, w(0)) approximate to delta(q) as delta -> 0(+), where q = q(v,p) is given explicitly as a funct...

With increasing fishing pressures having brought several stocks to the brink of collapse, there is a need for developing efficient harvesting methods that account for factors beyond merely yield or profit. We consider the dynamics and management of a stage-structured fish stock. Our work is based on a consumer-resource model which De Roos et al. (i...

In this paper, we consider equations of p-Laplace type of the form ∇⋅A(x,∇u)=0. Concerning A we assume, for p∈(1,∞) fixed, an appropriate ellipticity type condition, Hölder continuity in x and that A(x,η)=|η|p−1A(x,η/|η|) whenever x∈Rn and η∈Rn∖{0}. Let Ω⊂Rn be a bounded domain, let D be a compact subset of Ω. We say that uˆ=uˆp,D,Ω is the A-capaci...

A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also...

During the last century the hydropower units have been developed from a few megawatts per unit, up to several hundreds megawatts per unit. Over the years the operating conditions have also been changed from the ones that the machines were originally designed. These changes will significantly affect the lifespan of the machines. The hydropower plant...

Earlier measurements in large synchronous generators indicate the existence of complex whirling motion, and also deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse responses du...

In this paper we prove the boundary Harnack inequality for positive functions which vanish continuously on a portion of the boundary of a bounded domain Ω ⊂ R 2 and which are solutions to a general equation of p-Laplace type, 1 < p < ∞. We also establish the same type of result for solutions to the Aronsson type equation ∇(F (x, ∇u)) · F η (x, ∇u)...

The Silences of the Archives, the Reknown of the Story. The Martin Guerre affair has been told many times since Jean de Coras and Guillaume Lesueur published their stories in 1561. It is in many ways a perfect intrigue with uncanny resemblance, persuasive deception and a surprizing end when the two Martin stood face to face, memory to memory, befor...

Let Ω i ⊂ℝ n , i∈{1,2}, be two (δ,r 0 )-Reifenberg flat domains, for some 0<δ<δ ^ and r 0 >0, assume Ω 1 ∩Ω 2 =∅ and that, for some w∈ℝ n and some 0<r, w∈∂Ω 1 ∩∂Ω 2 , ∂Ω 1 ∩B(w,2r)=∂Ω 2 ∩B(w,2r). Let p, 1<p<∞, be given and let u i , i∈{1,2}, denote a non-negative p-harmonic function in Ω i , assume that u i , i∈{1,2}, is continuous in Ω ¯ i ∩B(w,2r...

Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to an...

In this paper we highlight a set of techniques that recently have been used to establish boundary Harnack inequalities for p-harmonic functions vanishing on a portion of the boundary of a domain which is 'flat' in the sense that its boundary is well-approximated by hyperplanes. Moreover, we use these techniques to establish new results concerning b...

Results from earlier measurements on hydropower generators have indicated relatively large eccentricities and shape deviations in the rotor and stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The UMP force can produce large vibrations which can be dangerous...

R. V. Bekryaev derived a system for a horizontally baroclinic atmosphere con-sisting of six ordinary differential equations. We prove dissipativity and find estimates for the location of the global attractor. The evolution of a compli-cated attractor is analysed with a Poincaré map showing difficult bifurcation behaviour. Investigations in bifurcat...