bluuebunny/crossref_metadata_2025_split huggingface dataset:
Exact and approximate boundary conditions at artificial boundaries
Authors: Lill Georg 
Published: October 2005

AbstractThe use of transformation methods for the derivation of boundary conditions at artificial boundaries had been initiated by Engquist and Majda [4. 5]. They considered the scalar wave equation and strictly hyperbolic systems. This has been extended by Gustafsson [11] to inhomogeneous conditions, by Hagstrom [15] to parabolic and Halpern et al. [17, 20] to incompletely parabolic systems. Here a systematic method is developed which unifies these approaches. Additionally, inhomogeneities with non‐compact support are taken into account. Exact and first‐order approximate boundary conditions for the compressible Navier–Stokes equations are presented.
Boundary conditions in acoustic scattering with respect to the reciprocity relation
Authors: Reissinger Jörg 
Published: October 2005

AbstractA new concept associated with the reciprocity relation in acoustic scattering is introduced. Motivated by this well‐known relation, which holds in all the classical cases, more general boundary value problems for the scalar Helmholtz equation are studied. These generalized boundary conditions are characterized by the validity of the reciprocity relation and seem to be an appropriate unification of a large class of boundary value problems in acoustic scattering. The well‐known results for the classical problems can be extended to this general case and also new connections with the question about existence and uniqueness of solutions to the boundary value problems can be derived. A constructive procedure shows that this approach is applicable for a large class of boundary conditions.
Schauder estimates for boundary layer potentials
Authors: Wiegner Michael 
Published: October 2005

AbstractBoundary layer potentials with Hölder‐continuous densities are widely used for representing solutions of boundary value problems for certain partial differential equations. These potentials are of the type
equation image
with |ρ| odd and a density λ of class Ck+α. This paper presents a self‐contained exposition of the fact that the potential v may be continued as Ck+α‐functions onto G and ℝn\G respectively (together with estimates for the Hölder‐norms) under the least possible regularity assumption for the boundary ∂G: it has to be of class Ck+1+α.
Weak solutions of the initial‐boundary value problem for the Vlasov–Poisson system
Authors: Abdallah Naoufel Ben 
Published: October 2005

AbstractIn this paper we show the existence of a weak solution of the boundary value problem for the time dependent Vlasov–Poisson system. First, we regularize the system in order to apply a fixed‐point theorem. Then we pass to the limit using an energy estimate.
A finite element method and stabilization method for a non‐linear tricomi problem
Authors: Lar'kin N. A. , Schneider M. 
Published: October 2005

AbstractWe prove using the Faedo‐Galerkin method the existence of a generalized solution of an initial‐boundary value problem for the non‐linear evolution equationmagnified image0 ⩽ Q ⩽ 2, in a cylinder QT = Ω × (0, T), where 𝒯 u = yuxx + uyy is the Tricomi operator and l(u) a special differential operator of first order. We then show that the approximate generalized solution of problem (*) converges to the approximate generalized solution of the corresponding stationary boundary value problem as t → ∞.
Approximation of solutions to evolution equations
Authors: Miletta Peter D. 
Published: October 2005

AbstractThe convergence of the Galerkin approximations to solutions of abstract evolution equations of the form u′(t)= − Au(t) + M(u(t)) is shown. Here A is a closed, positive definite, self‐adjoint linear operator with domain D(A) dense in a Hilbert space H and M is a non‐linear map defined on D(A½) which satisfies a Lipschitz condition on balls in D(A½).
On a semi‐coercive problem in a porous journal bearing with cavitation problem as boundary condition and subject to an integral condition
Authors: Boukrouche Mahdi 
Published: October 2005

AbstractWe study a non‐linear problem in pressure saturation modelling of a free boundary problem, arising in self‐lubricating bearings, with Neumann boundary conditions for the pressure and a non‐local constraint on the saturation variable, which indeed is a Lagrange multiplier. We prove an existence theorem by introducing an artificial time dependence and using the pseudo‐characteristics discretization method and semi‐coercive variational inequalities.
Unique solvability of the periodic Cauchy problem for wave‐hierarchy problems with dissipation
Authors: Göz Manfred F. 
Published: October 2005

AbstractWave‐hierarchy problems appear in a variety of applications such as traffic flows, roll waves down an open inclined channel and multiphase flows. Usually, these are described by the compressible Navier‐Stokes equations with specific non‐linearities; in a fluidized bed model they contain an additional pressure gradient term and are supplemented by an elliptic equation for this unknown pressure. These equations admit solutions periodic in space as well as in time, i.e. periodic travelling waves. Therefore, the corresponding initial value problem with periodic boundary conditions is solved locally in time in appropriate Sobolev spaces. Some remarks are made concerning global solutions, the occurrence of clusters or voids and the bifurcation of time periodic solutions, respectively.
Two canonical wedge problems for the Helmholtz equation
Authors: Meister E. , Penzel F. , Speck F.‐O. , Teixeira F. S. 
Published: October 2005

AbstractBoundary‐transmission problems for two‐dimensional Helmholtz equations in a quadrant and its complement, respectively, are considered in a Sobolev space setting. The first problem of a quadrant with Dirichlet condition on one face and transmission condition on the other is solved in closed form for the case where all the quadrants are occupied by the same medium. Unique solvability can also be shown in the case of two different media up to exceptional cases of wave numbers, while the Fredholm property holds in general. In the second problem, transmission conditions are prescribed on both faces. Similar results are obtained in the one‐medium case, but the two‐media case turns out to be more complicated and the equivalent system of boundary pseudodifferential equations cannot be completely analysed by this reasoning.
On identification of memory kernels in linear theory of heat conduction
Authors: von Wolfersdorf L. 
Published: October 2005

AbstractA linear integrodifferential equation describing the heat flow in a material with memory is considered. This equation contains a pair of time‐dependent convolution kernels that are unknown. Such kernels are determined as solutions of an optimal control problem by using additional data obtained from measurements of average temperature around some fixed points of the domain over some finite time interval. We show the existence of an optimal solution of this problem and derive optimality conditions for it.
Quantitative error estimates for coefficient idealization in linear elliptic problems
Authors: Han Weimin 
Published: October 2005

AbstractWe give a thorough quantitative error analysis for the effect of coefficient idealization on solutions of linear elliptic boundary value problems. The a posteriori error estimate is derived by a tactful application of the duality theory in convex analysis. The estimate involves an auxiliary function subject to certain constraint. We discuss in detail the selection of a good auxiliary function for various cases. Numerical examples show the effectiveness of our a posteriori error estimate.
On the boundary transmission problem of thermoelastostatics in a plane domain with interface corners
Authors: Jentsch Lothar 
Published: October 2005

AbstractThis paper deals with bimetal problems of thermoelastostatics. By means of an explicit particular solution a reduction to problems of elastostatics is given. An indirect boundary integral method is applied for solving the traction boundary value problem. The solution is represented by a potential of single layer type having Green's contact tensor as the kernel. Thus, from the first the transmission conditions are satisfied. The Fredholm property of the boundary integral operator as well as the asymptotics of the potential density at an interface corner depend on the symbol of a Mellin convolution operator. The singular functions at corners can be obtained by calculating the potential for terms in the asymptotic expansion of the density.
Stokes flow of a micropolar fluid exterior to several non‐intersecting closed surfaces, but contained by an exterior contour
Authors: Power Henry , Ramkissoon Harold 
Published: October 2005

AbstractThe problem of determining the Stokes flow of a micropolar fluid exterior to several closed surfaces but contained by an exterior contour that encloses all the interior surfaces, is formulated as a system of linear Fredholm integral equations of the second kind. These integral equations are obtained when the velocity and microrotation vector fields are represented by a double‐layer potential with unknown density, and certain singular solutions of the Stokes' micropolar equations. This double‐layer potential is defined over the union of all the surfaces involved including the exterior contour. The singularities, corresponding to a concentrated force and concentrated couple located within each interior surface, give rise to force and torque whose magnitudes are linearly dependent on the unknown density of the double layer. It is shown that the system possesses a unique continuous solution when the boundaries are Lyapunov surfaces and the boundary data is continuous.
Reciprocity relations and completeness of far‐field pattern vectors for obstacle scattering of acoustic wave in a stratified medium
Authors: Xu Yongzhi 
Published: October 2005

AbstractUnder a generalized Sommerfeld radiation condition, we proved the uniqueness and existence of the direct obstacle scattering problem of time‐harmonic acoustic waves in a stratified medium [8]. In this paper, we study the asymptotic behaviour of the scattered waves and prove three reciprocity relations among the free‐wave far‐field patterns and the guided‐wave far‐field pattern vectors corresponding to incident distorted plane waves and normal mode waves. Then we prove conditions under which a set of far‐field patterns is complete in a Hilbert space based on the reciprocity relation. These properties are important in investigating the inverse obstacle scattering problems.
Non‐orthogonal expansions on the sphere
Authors: Freeden Willi , Schreiner Michael 
Published: October 2005

AbstractDiscrete families of functions with the property that every function in a certain space can be represented by its formal Fourier series expansion are developed on the sphere. A Fourier‐series‐type expansion is obviously true if the family is an orthonormal basis of a Hilbert space, but it also can hold in situations where the family is not orthogonal and is ‘overcomplete’. Furthermore, all functions in our approach are axisymmetric (depending only on the spherical distance) so that they can be used adequately in (rotation) invariant pseudo‐differential equations on the sphere. The three classes of examples particularly studied here are (i) Abel‐Poisson frames (ii) Gauss‐Weierstrass frames and (iii) frames consisting of locally supported kernel functions. Abel‐Poisson frames form families of harmonic functions and provide us with powerful approximation tools in potential theory. Gauss‐Weierstrass frames are intimately related to the diffusion equation on the sphere and play an important role in multiscale descriptions of image processing on the sphere. The third class enables us to discuss spherical ‘Fourier expansions’ by means of ‘axisymmetric finite elements’.
On the sharp singular limit for slightly compressible fluids
Authors: Beirão da Veiga H. 
Published: October 2005

AbstractWe consider the equations of motion to slightly compressible fluids and we prove that solutions converge, in the strong norm, to the solution of the equations of motion of incompressible fluids, as the Mach number goes to zero. From a physical point of view this means the following. Assume that we are dealing with a well‐specified fluid, so slightly compressible that we assume it to be incompressible. Our result means that the distance between the (continuous) trajectories of the real and of the idealized solution is ‘small’ with respect to the natural metric, i.e. the metric that endows the data space.
The double layer potential method for a boundary transmission problem for the Laplace operator in an infinite wedge
Authors: Mirschinka Dirk 
Published: October 2005

AbstractThis paper is concerned with the solution of a boundary transmission problem in an infinite wedge. We treat this problem by a boundary integral method using Green's contact function for two half‐spaces. The integral operators are studied via a harmonic analysis approach which goes back to a paper of Fabes et al. We improve their results studying the Fourier symbol of the associated integral operators on the half‐plane. This leads to invertibility criteria for the boundary integral operators.
Calculation of microstrains and microstresses in a thick non‐symmetric heterogeneous plate by homogenization
Authors: Tapiéro Roland 
Published: October 2005

AbstractWe consider the thermoelastic behaviour of a thick heterogeneous plate containing in its thickness a large number of periodically distributed transverse holes or inclusions. We use the Reissner‐Mindlin thermoelastic linear model of thick plates with a known temperature and we distinguish displacements in the upper and lower part of the plate with respect to the middle plane. Due to the structure of the plate, thermal and elastic coefficients are non‐uniformly and rapidly oscillating functions of the space variable. Two‐scale convergence, which is the state of the art in mathematical homogenization technics, is used and gives convergence results and formulae allowing to calculate the distribution of microstrains and microstresses inside the plate when a macroscopic behaviour is given.
Global in time existence of small solutions of non‐linear thermoviscoelastic equations
Authors: Shibata Yoshihiro 
Published: October 2005

AbstractWe prove a global in time existence theorem of classical solutions of the initial boundary value problem for a non‐linear thermoviscoelastic equation in a bounded domain for very smooth initial data, external forces and heat supply which are very close to a specific constant equilibrium state. Our proof is a combination of a local in time existence theorem and some a priori estimates of local in time solutions. Such a priori estimates are proved basically for suitable linear problems by using some multiplicative techniques. An exponential stability of the constant equilibrium state also follows from our proof of the existence and regularity theorems.
A discrete velocity coagulation‐fragmentation model
Authors: Slemrod M. , Qi A. , Grinfeld M. , Stewart I. 
Published: October 2005

AbstractA discrete velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in a volume V with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker‐Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. Results of numerical experiments are presented.
Weak solutions to a non‐linear hyperbolic system arising in the theory of dielectric liquids
Authors: Feireisl Eduard 
Published: October 2005

AbstractWe consider a model of the motion of a viscous dielectric liquid subjected to a DC electric field in the case when the bulk conduction results from the presence of a dissociation‐recombination process. The effects of both magnetic field and ionic diffusion are neglected. The existence of at least one weak solution is proved via the method of renormalized solutions.
On a local in time solvability of the Neumann problem of quasilinear hyperbolic parabolic coupled systems
Authors: Dan Wakako 
Published: October 2005

AbstractWe prove a local in time existence theorem of classical solutions to some coupled system of quasilinear hyperbolic equations and quasilinear parabolic equations with Neumann boundary condition. This coupled system contains a non‐linear thermoelastic equation as an important physical example.
Skin biopsy and quantitative sensory testing do not predict response to lidocaine patch in painful neuropathies
Authors: Herrmann David N. , Pannoni Valerie , Barbano Richard L. , Pennella‐Vaughan Janet , Dworkin Robert H. 
Published: October 2005

AbstractPredictors of response to neuropathic pain treatment in patients with painful distal sensory neuropathies are lacking. The 5% lidocaine patch is believed to exert its effects on neuropathic pain via a local stabilizing effect on cutaneous sensory afferents. As such, it provides a model to assess whether the status of epidermal innervation as determined by skin biopsy or quantitative sensory testing (QST) of small‐ and large‐diameter sensory afferents might serve as predictors of response to topical, locally active treatment. In this study we assessed associations between epidermal nerve fiber (ENF) densities, sensory nerve conduction studies (NCS), QST, and response to a 5% lidocaine patch in patients with painful distal sensory neuropathies. We observed no association between distal leg epidermal and subepidermal innervation and response to the lidocaine patch. Several patients with complete loss of distal leg ENF showed a response to the lidocaine patch. Similarly we observed no consistent association between treatment response and QST for vibration, cooling, warm, heat‐pain, and cold‐pain thresholds, or distal sensory NCS. Thus, distal‐leg skin biopsy, QST, and sensory NCS cannot be used to identify patients with painful polyneuropathy likely to respond to a lidocaine patch in clinical practice. Further studies are required to clarify precisely the mechanism and site of action of the lidocaine patch in patients with peripheral neuropathic pain. Muscle Nerve, 2005
Gene‐based treatment of motor neuron diseases
Authors: Federici Thais , Boulis Nicholas M. 
Published: October 2005

AbstractMotor neuron diseases (MND), such as amyotrophic lateral sclerosis (ALS) and spinal muscular atrophy (SMA), are progressive neurodegenerative diseases that share the common characteristic of upper and/or lower motor neuron degeneration. Therapeutic strategies for MND are designed to confer neuroprotection, using trophic factors, anti‐apoptotic proteins, as well as antioxidants and anti‐excitotoxicity agents. Although a large number of therapeutic clinical trials have been attempted, none has been shown satisfactory for MND at this time. A variety of strategies have emerged for motor neuron gene transfer. Application of these approaches has yielded therapeutic results in cell culture and animal models, including the SOD1 models of ALS. In this study we describe the gene‐based treatment of MND in general, examining the potential viral vector candidates, gene delivery strategies, and main therapeutic approaches currently attempted. Finally, we discuss future directions and potential strategies for more effective motor neuron gene delivery and clinical translation. Muscle Nerve, 2005
Intracellular signaling during skeletal muscle atrophy
Authors: Kandarian Susan C. , Jackman Robert W. 
Published: October 2005

AbstractA variety of conditions lead to skeletal muscle atrophy including muscle inactivity or disuse, multiple disease states (i.e., cachexia), fasting, and age‐associated atrophy (sarcopenia). Given the impact on mobility in the latter conditions, inactivity could contribute in a secondary manner to muscle atrophy. Because different events initiate atrophy in these different conditions, it seems that the regulation of protein loss may be unique in each case. In fact differences exist between the regulation of the various atrophy conditions, especially sarcopenia, as evidenced in part by comparisons of transcriptional profiles as well as by the unique triggering molecules found in each case. By contrast, recent studies have shown that many of the intracellular signaling molecules and target genes are similar, particularly among the atrophies related to inactivity and cachexia. This review focuses on the most recent findings related to intracellular signaling during muscle atrophy. Key findings are discussed that relate to signaling involving muscle ubiquitin ligases, the IGF/PI3K/Akt pathway, FOXO activity, caspase‐3 activity, and NF‐kappaB signaling, and an attempt is made to construct a unifying picture of how these data can be connected to better understand atrophy. Once more detailed cellular mechanisms of the atrophy process are understood, more specific interventions can be designed for the attenuation of protein loss. Muscle Nerve, 2006
Selective activation of the sacral anterior roots for induction of bladder voiding
Authors: Bhadra Narendra , Grünewald Volker , Creasey Graham H. , Mortimer J. Thomas 
Published: October 2005

AbstractAimWe investigated the efficacy of selective activation of the smaller diameter axons in the sacral anterior roots for electrically induced bladder voiding.Materials and MethodsAcute experiments were conducted in five adult dogs. The anterior sacral roots S2 and S3 were implanted bilaterally with tripolar electrodes. Pressures were recorded from the bladder and from the proximal urethra and the external urethral sphincter. A detector and flow meter monitored fluid flow. A complete sacral dorsal rhizotomy was carried out. The effects of two types of pulse trains at 20 Hz were compared; quasitrapezoidal pulses (500 µsec with 500 µsec exponential decay) and interrupted rectangular (100 µsec, 2 sec on/2 sec off). Before rhizotomy, rectangular pulse trains (100 µsec) to activate all fibers were also applied. The experimental design was block randomized before and after rhizotomy.ResultsQuasitrapezoidal pulses showed block of sphincter activation with average minimum current for maximum suppression of 1.37 mA. All pulse types evoked average bladder pressures above the basal sphincter closure pressure. The pressure patterns in the proximal urethra closely followed the bladder pressures. Before dorsal rhizotomy, stimulation evoked a superadded increase in sphincter pressures with slow rise time. After rhizotomy, the sphincter pressure patterns followed the bladder pressures during selective activation and voiding occurred during stimulation with quasitrapezoidal trains and in between bursts with interrupted rectangular stimulation.ConclusionsSelective activation of sacral ventral roots combined with dorsal rhizotomy may provide a viable means of low‐pressure continuous voiding in neurological impairment. Neurourol. Urdynam. © 2005 Wiley‐Liss, Inc.
A row relaxation method for large ℓp least norm problems
Authors: Dax Achiya 
Published: October 2005

AbstractThis paper presents a row relaxation method for solving the regularized ℓp least norm problem

where e and p are positive constants, 1<p<∞ The interest that we have in this problem lies in the observation that for small values of E the minimizer of P (X ) is a good substitute for a minimizer of the unregularized problem

It is shown that the dual of the regularized problem has the form

where q = p /(p ‐ 1). Moreover, if y solves the dual problem then X = ATy/ϵ solves the primal problem and P(ATy/ϵ) = D(y). Maximizing the dual objective function by changing one variable at a time results in a row relaxation method that resembles Kaczmarz's method. This feature makes the new method suitable for solving large sparse C, problems that arise in computerized tomography, geophysics, and groundwater hydrology. Numerical experiments illustrate the feasibility of our ideas.