bluuebunny/crossref_metadata_2025_split huggingface dataset:
Lösungen der poissongleichung und harmonische vektorfelder in unbeschränkten gebieten
Authors: Mäulen J. , Werner P. 
Published: March 2007

AbstractIn the first part of this paper we consider generalised solutions of the Poisson equation ΔU=Fin open subsets ofRn(n⩾ 3) with Dirichlet or Neumann boundary data. We prove existence and uniqueness theorems, not only for the corresponding interior and exterior problems, but also for domains with boundaries extending to infinity. In the second part we discuss generalised harmonic fields in open subsets ofR3with vanishing Dirichlet or Neumann boundary condition.
Global topological perturbations of nonlinear elliptic eigenvalue problems
Authors: Peitgen H. O. , Schmitt K. , Kirchgassner K. 
Published: March 2007

AbstractThis paper is concerned with bifurcation from infinity for nonlinear elliptic equations, which are not necessarily linearizable at infinity. The methods employed are global perturbation techniques by means of which one obtains access to continua of positive solutions bifurcating from infinity via continua bifurcating from trivial solutions.
Galerkin approximations for the one‐dimensional vlasov‐poisson equation
Authors: Cooper J. , Neunzert H. 
Published: March 2007

AbstractBy taking Fourier series in the space variable, and truncating, we construct a Galerkin scheme for approximate solutions to the one dimensional Vlasov‐Poisson equation. Existence is proved for the approximate solutions and they are shown to converge to an exact solution in a weak sense.
Variational derivatives and p‐gradients of functionals on spaces of continuously differentiable functions
Authors: Hamilton E. P. , Nashed M. Z. , Brosowski B. 
Published: March 2007

AbstractThe purpose of this paper is to introduce and study a new type of derivative – the variational gradient – for a functional on Cn[a, b]. Local and global versions of this concept are analyzed. This notion provides a natural approach to variational derivatives on Cn[a, b] under rather mild smoothness assumptions on the functional. When applied in the context of the Calculus of Variations, the notion of the variational gradient captures the natural boundary conditions (as well as the Euler‐Lagrange equations) under weaker smoothness assumptions than those usually required using Gǎteaux variations.Conditions are established for the existence of the variational derivative and an integral representation for the Gǎteaux variation in terms of the variational derivative is derived. Conditions for the variational derivative to be differentiable are also established.
Ein resonanzphänomen in der theorie akustischer und elektromagnetischer wellen
Authors: Werner P. 
Published: March 2007

AbstractWe discuss the asymptotic behaviour of acoustic and electromagnetic waves, generated by given time‐harmonic exterior forces with frequency ω, in the unbounded region between the parallel planes X3 = 0 and X3 = 1, and show that the principle of limiting amplitude is violated if ω = πn(n = 1, 2,…). For these values of the frequency, forces with compact support can be chosen such that the amplitudes of the waves increase with a logarithmic rate as t → ∞.
On the transmission problem of the helmholtz equation for quadrants
Authors: Latz N. , Meister E. 
Published: March 2007

AbstractThe plane transmission problem of the Helmholtz equation for quadrants is characterized by a one‐dimensional singular integral equation, which refers to the Fourier transform of the normal derivative of the solution along the x‐axis. It is derived by solving the transmission problem for the upper and the lower half‐plane involving a Neumann condition at y = 0. This is done by a two‐dimensional Laplace transform technique. The inverse Laplace transform with respect to the second cartesian coordinate and the restriction of this one to y = 0 then lead to the integral equation. Thereby the transmission conditions of the original problem at y = 0 have to be taken into account. The resulting integral equation is of generalized Wiener‐Hopf‐type. It is solved via the contraction theorem imposing restricting conditions on the wave numbers.
Thin elastic and periodic plates
Authors: Caillerie D. , Nedelec J. C. 
Published: March 2007

AbstractThis paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e → 0 then ω → 0), (ω → 0 then e → 0) and lately (e and ω → 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.
An existence theorem for compressible viscous and heat conducting fluids
Authors: Łukaszewicz G. , Piskorek A. 
Published: March 2007

AbstractWe consider an initial‐boundary value problem of a flow of a viscous and heat‐conducting gas in a bounded domain D ⊂ R3. We assume that the boundary S of D consists of two disjoint surfaces S1 and S2 of class C2, and that the gas enters D through the surface S1 and leaves D through the surface S2.Our aim is to prove the existence (locally in time) of a solution of the problem in anisotropic Sobolev spaces.
Exact and chapman‐enskog solutions for the carleman model
Authors: Palczewski A. , Neunzert H. 
Published: March 2007

AbstractThe Chapman‐Enskog procedure is applied to the Carleman model of the Boltzmann equation. It has been proved that the Carleman equations possess a solution on the time interval on which a smooth solution of the fluid‐like equation exists. The calculations have been performed up to the first order i.e., to the Navier‐Stokes‐like equation. It has been shown that in this case a difference between an exact solution and the Chapman‐Enskog solution is of order ϵ2. Extension of the results to higher orders is also possible. This gives a justification of the Chapman‐Enskog procedure as an asymptotic expansion method.
On the geometric form of free boundaries satisfying a bernoulli condition
Authors: Acker A. , Payne L. E. 
Published: March 2007

AbstractIn the x–y plane, let Ω denote an annular domain bounded by the simple closed curves ⌜ and ⌜*, such that the capacity potential U in Ω satisfies ∣ ▽ U∣ = 1 on ⌜. Assuming ⌜* to be known, we obtain qualitative properties of ⌜. For example, the number of local maxima or minima of the y‐co‐ordinate relative to ⌜ cannot exceed the corresponding number for ⌜*.
An error analysis of the tau method for a class of singularly perturbed problems for differential equations
Authors: Ortiz E. L. , Pham‐Ngoc‐Dinh A. , Törnig W. 
Published: March 2007

AbstractBy using classical results of Poincaré and Birkhoff we discuss the existence and uniqueness of solution for a class of singularly perturbed problems for differential equations. The Tau method formulation of Ortiz [6] is applied to the construction of approximate solutions of these problems. Sharp error bounds are deduced.These error bounds are applied to the discussions of a model problem, a simple one‐dimensional analogue of Navier‐Stokes equation, which has been considered recently by several authors (see [2], [3], [8], [10]). Numerical results for this problem [8] show that the Tau method leads to more accurate approximations than specially designed finite difference or finite element schemes.
Exact bounds for the radially symmetric shape of confined plasma in the unit circle
Authors: Hoffmann K.‐H. , Sprekels J. , Hsiao G. 
Published: March 2007

AbstractThe method of “cone iteration”; is used to obtain exact bounds for the solutions of a class of nonlinear operator equations. The general theory is applied to the problem of finding radially symmetric solutions of the plasma problem in the unit circle. Existence and uniqueness results are obtained at the same time. Some numerical examples demonstrate the method's high degree of accuracy.
Finite elements for the eigenvalue problem of differential operators in unbounded intervals
Authors: Höhn W. , Törnig W. 
Published: March 2007

AbstractThe eigenvalue problem for one‐dimensional differential operators with a possible essential spectrum is discretized with finite elements defined on a bounded interval together with a fundamental system of the differential equation outside of the interval. A non‐pollution property of the discrete spectra is proved and the error in the approximation of isolated eigenvalues and corresponding eigenvectors is estimated. The convergence of some numerical algorithms for the solution of the subsequent discrete nonlinear eigenvalue problem is proved. The method is tested in some numerical examples.
A fast solver for riemann problems
Authors: Halter E. , Martensen E. 
Published: March 2007

AbstractAn efficient algorithm is presented for solving the Riemann problem for a polytropic gas. It enables the user to compute the solution for all physically reasonable data. The convergence of the algorithm is proved. The accuracy of the solution is limited only by the accuracy of the computer. There is an a‐priori estimation of the required number of iterations. The rate of convergence turns out to be much higher than that of the usual fixed point iteration scheme.
Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity
Authors: Levine H. A. , Protter M. H. , Payne L. E. 
Published: March 2007

AbstractLower bounds for the eigenvalues of some elliptic equations and elliptic systems over bounded regions are obtained. The bounds are universal in that they depend only upon the volume of the region. Specific applications include the clamped plate, the buckling problem for the clamped plate and the equations of linear elasticity.Our results are consequences of extensions of the methods of Li and Yau (Comm. Mat. Phys. 88 (1983) 309–318) who obtained such results for the eigenvalues of the fixed membrane problem.
On a free boundary value problem of physical geodesy, I (uniqueness)
Authors: Witsch Karl J. , Leis R. 
Published: March 2007

AbstractThe determination of the figure of the earth is considered as a local free boundary value problem of potential theory: the shape of a slowly rotating heavy body has to be found from the boundary data of the attracting force and its potential outside of the body, provided that an approximation to the solution is already known. In this paper a uniqueness result is proved which is local with respect to theC1‐topology.
A note on the solvability of Boltzmann's equation via comparison methods
Authors: Wieser W. , Neunzert H. 
Published: March 2007

AbstractWe consider the Cauchyproblem for the space‐inhomogeneous Boltzmann equation. For the so‐called soft‐interaction case we prove unique local solvability, analogous to a result of Palczewski [1]. However, since in our proof a comparison argument is used rather than the familiar contraction mapping principle, we are able to extend the previously known time‐interval of existence. In a final section the two main difficulties in generalizing the result are discussed in some detail.
Relative influence of two small parameters in non uniformly elliptic homogenization problems
Authors: Paulin J. Saint Jean , Eckhaus W. 
Published: March 2007

AbstractWe study three elliptic problems depending on two small parameters (ϵ = homogenization parameter and δ = perturbation parameter which causes non uniform ellipticity). In each case, the homogenized operator corresponding to the second order operator is independent of the way (ϵ, δ) → (0, 0), but the convergence results and the limit solution do depend on the relative size of ϵ and δ; the relevant parameter is δϵ−2.
Examples involving the geometric form of level curves of harmonic functions
Authors: Acker A. , Payne L. 
Published: March 2007

AbstractIn the x‐y plane, we give, for example, a Jordan curve Γ containing exactly one local maximum and one local minimum in the y‐direction, such that some level curve of the capacity potential in the exterior complement of Γ has at least n local maxima and n local minima in the y‐direction, n being any prescribed number.
Optimal bounds for bilinear forms associated with linear equations
Authors: Mika J. , Pack D. C. , Cole R. J. , Roach G. F. 
Published: March 2007

AbstractThe construction of upper and lower bounds to the bilinear quantity g0, f, where f is the solution of an operator equation Tf = f0, requires either an approximation for f or one for T−1. In this paper the question of “best” approximation of T−1 by an operator of the form B = βI, where β is a real constant, is investigated for linear operators that are either self‐adjoint or can be related by suitable manipulations to others that are. Particular attention is paid to a special operator, previously studied by Robinson, of importance in predicting the dynamic polarisabilities of quantum‐mechanical systems.
An optimal design problem for submerged bodies
Authors: Angell T. S. , Hsiao G. C. , Kleinman R. E. 
Published: March 2007

AbstractThe problem of finding the shape of a smooth body submerged in a fluid of finite depth which minimizes added mass or damping is considered. The optimal configuration is sought in a suitably constrained class so as to be physically meaningful and for which the mathematical problem of a submerged body with linearized free surface condition is uniquely solvable. The problem is formulated as a constrained optimization problem whose cost functional (e.g. added mass) is a domain functional. Continuity of the solution of the boundary value problem with respect to variations of the boundary is established in an appropriate function space setting and this is used to establish existence of an optimal solution. A variational inequality is derived for the optimal shape and it is shown how finite dimensional approximate solutions may be found.
The two‐dimensional, linear, orthotropic plate: The traction problem
Authors: Gilbert R. P. , Schneider M. 
Published: March 2007

AbstractIn [13] we extended the analysis of Ciarlet and Destuynder [5] to the clamped orthotropic plate. For the present paper we shall apply these methods to the orthotropic plate under traction. In particular, we shall be considering the type of problem posed in Friedrichs and Dressler [10] for the isotropic plate and make use of the fact that the variational problem will split just as was the case for the partial differential equation formulation. With the present approach we shall be able to produce a proper convergence analysis for the formal asymptotics used in Friedrichs and Dressler.
On the computer implementation of a coupled boundary and finite element method for the bidimensional exterior steady stokes problem
Authors: Sequeira Adélia , Lisboa  , Palaiseau  , Nedelec J. C. 
Published: March 2007

AbstractA numerical technique based on the coupling of boundary and finite element methods has been developed by the author for the steady Stokes problem in an unbounded domain. The present paper deals with the implementation of the coupled program in the two‐dimensional case. Computational results are given for a particular problem which can be seen as a good test case for the accuracy of the method.
On optimal shape design of systems governed by mixed Dirichlet‐Signorini boundary value problems
Authors: Haslinger J. , Neittaanmäki P. , Meister E. 
Published: March 2007

AbstractA problem for finding optimal shape for systems governed by the mixed unilateral boundary value problem of Dirichlet‐Signorini‐type is considered. Conditions for the solvability of the problem are stated when a variational inequality formulation and when a penalty method is used for solving the state problem in question. The asymptotic relation of design problems based on these two formulations is presented. The optimal shape design problem is discretized by means of finite element method. The convergence results for the approximation are proved. The discretized versions are then formulated as a non‐linear programming problem. Results of practical computations of the problem in question are reported.
Periodic solutions of quasilinear non‐autonomous systems with impulses
Authors: Hristova S. G. , Bainov D. D. , Roach G. F. 
Published: March 2007

AbstractThe paper considers a system of differential equations with impulse perturbations at fixed moments in time of the formmagnified imagewhere x ϵ Rn, ε is a small parameter,Sufficient conditions have been found for existence of the periodic solution of the given system in the critical and non‐critical cases.
On the determination of the worst sampling error in a communication system for pulse‐amplitude‐modulated signals by solving an approximation problem
Authors: Krabs W. , Meister E. 
Published: March 2007

AbstractA communication system for pulse‐amplitude‐modulated signals is considered whose impulse response is bandlimited. For a certain class of sampling errors the worst case is investigated where the sampling error of the system is such that the least mean square transmission error achieved by a suitable choice of the impulse response becomes maximal. This problem is dualized in the sense of two person game theory and thereby transferred to an equivalent approximation problem for whose solution a necessary and sufficient condition is given and applied to special cases.
The influence of a geographical barrier on the balance of selection and migration
Authors: van der Meer J. J. E. , Roach G. F. 
Published: March 2007

AbstractIn biology, a cline is defined as a usually gradual change in gene frequency or phenotype of a population in equilibrium, from one place to another.We define a cline as a nonconstant stable steady state solution. However, for the model studied in this paper, these two definitions coincide: a nonconstant stable steady state solution is necessarily monotone. It is proved that for small values of the penetrability of the barrier, exactly two clines exist.Since we prove that the Ω‐limit set of any initial condition is a steady state solution, the information thus obtained yields a rather complete understanding of the qualitative behaviour of the solutions of the evolution problem under consideration.
Formulation variationnelle espace‐temps pour le calcul par potentiel retardé de la diffraction d'une onde acoustique (I)
Authors: et T. Ha Duong A. Bamberger , Nedelec J. C. 
Published: March 2007

AbstractWe give here a space‐time variational formula to the problem of the transient acoustic scattering by a free (pressure release) surface, using the retarded potential technique. From this formula, we obtain new schemes for the calculation of the potential density. We prove stability and convergence of such schemes: these are as far as we know, the first results in that direction for such problem. The case of a hard obstacle will be treated in the second part of the paper.
The low frequency limit for time‐harmonic acoustic waves
Authors: Picard R. , Leis R. 
Published: March 2007

AbstractThe question of convergence of the solution of the exterior Dirichlet boundary value problem of the first order system of linearized acoustics as the frequency ω tends to zero is considered. The particular difficulty of having zero as an eigenvalue is handled by introducing certain scalar characteristics that — if prescribed — imply uniqueness in the limit case ω = 0. Convergence to the static solution in a weighted L2‐space is shown. Eventually the convergence result obtained can be extended to a larger class of boundary value problems of Mathematical Physics due to the structure of the argument.
An algorithm for tracing the boundary curves of mushy regions in some degenerate diffusion problems
Authors: de Mottoni P. , Santi E. , Hadeler K.‐P. 
Published: March 2007

AbstractWe present an algorithm for approximating the solution of the degenerate diffusion problem ut = (ϕ(u))xx in (0,1) × R+ (with zero Dirichlet boundary conditions, and nonnegative initial datum u0), where ϕ(u) = min {ku1} for some ϰ > 0. The algorithm also provides an approximation for the interface curves which represent the boundary of the Mushy Region 𝔐 = {(x, t): ϕ (u(x, t)) = 1}. The convergence of the algorithm is proved.
On the simulation source technique for exterior problems in acoustics
Authors: Kress R. , Mohsen A. , Brosowski B. 
Published: March 2007

AbstractFor the solution of the exterior Dirichlet problem for the Helmholtz equation we propose to seek the solution in the form of an acoustic single‐layer potential with a distribution extended over an internal surface. This leads to an ill‐posed integral equation of the first kind which can be approximately solved by the Tikhonov regularization technique.
Formulation variationnelle pour le calcul de la diffraction d'une onde acoustique par une surface rigide
Authors: et T. Ha Duong A. Bamberger , Nedelec J. C. 
Published: March 2007

AbstractThis work is a continuation of [1]. We give a space‐time variational formula to the problem of the scattered acoutic wave by a hard body, using the double layer retarded potential technique. New schemes are constructed from this variationnal formula, for which we prove the stability and errors estimates.
A boundary integral equation method for three‐dimensional crack problems in elasticity
Authors: Stephan E. P. , Wendland W. L. 
Published: March 2007

AbstractThis paper presents a solution procedure for three‐dimensional crack problems via first kind boundary integral equations on the crack surface. The Dirichlet (Neumann) problem is reduced to a system of integral equations for the jump of the traction (of the field) across the crack surface. The calculus of pseudodifferential operators is used to derive existence and regularity of the solutions of the integral equations. With the concept of the principal symbol and the Wiener‐Hopf technique we derive the explicit behavior of the densities of the integral equations near the edge of the crack surface. Based on the detailed regularity results we show how to improve the boundary element Galerkin method for our integral equations. Quasi‐optimal asymptotic estimates for the Galerkin error are given.
On the convergence of the spline collocation with discontinuous data
Authors: Saranen J. , Wendland W. 
Published: March 2007

AbstractIn this article we study the convergence of the collocation method in the case where the smoothest splines are used as trial functions. The given data is allowed to be piecewise continuous. Our model problem is stated by means of an explicit Fourier representation in the space of periodic functions. Thus the results are applicable e.g. to differential operators and to classical integral operators of the convolutional type. Error estimates are given for a class of Sobolev norms. An application to the single layer potential is discussed.
Resonances and standing waves
Authors: Morgenröther K. , Werner P. 
Published: March 2007

AbstractRecent investigations on aperiodic waves, which are generated by time‐harmonic forces in waveguides, indicate a close relationship between resonances and certain time‐harmonic solutions of homogeneous boundary value problems for the wave equation (“standing waves”). This paper is motivated by the observation that, in all known cases, standing waves are connected with resonances if and only if they are subject to suitable asymptotic restrictions as |x| → ∞. These asymptotic properties are used to introduce a class of “admissible” standing waves. We prove that admissible standing waves do not exist in a certain class of local perturbations Ω of the n‐dimensional domain Ω0 bounded by the hyperplanes xn = 0 and xn = π. This extends a result of M. Faulhaber on the absence of eigenvalues. As we shall show in a subsequent paper, absence of admissible standing waves implies absence of resonances.