bluuebunny/crossref_metadata_2025_split huggingface dataset:
Boundary integral equations for mixed Dirichlet, Neumann and transmission problems
Authors: Von Petersdorff T. , Leis R. 
Published: August 2005

AbstractWe consider a Helmholtz equation in a number of Lipschitz domains inn≥ 2 dimensions, on the boundaries of which Dirichlet, Neumann and transmission conditions are imposed. For this problem an equivalent system of boundary integral equations is derived which directly yields the Cauchy data of the solutions. The operator of this system is proved to be injective and strongly elliptic, hence it is also bijective and the original problem has a unique solution. For two examples (a mixed Dirichlet and transmission problem and the transmission problem for four quadrants in the plane) the boundary integral operators and the treatment of the compatibility conditions are described.
Quasilinear hyperbolic‐hyperbolic singular perturbation problem: Study of shock layer
Authors: Garbey M. , Eckhaus W. 
Published: August 2005

AbstractWe present the asymptotic analysis of a quasilinear hyperbolic–hyperbolic singular perturbation problem in one dimension. The leading part of the analysis concerns the construction of some shock layers associated with discontinuities of a hyperbolic problem. This study is a generalization of the case of viscous perturbation for a hyperbolic problem.
Admissibility and uniqueness of weak solutions to hyperbolic systems of balance laws
Authors: Kosiński Witold , Brosowski B. 
Published: August 2005

AbstractA system of quasi‐linear first‐order equations written in the divergence form and constrained by the unilateral differential inequality (the second law of thermodynamics) with a strictly concave entropy function is analysed. In the class BV, i.e. a subset of regular distributions represented by functions of bounded variation in the sense of Tonelli‐Cesari, a weak solution to the system is defined. The parabolized version of the system is also discussed in order to define an admissible weak solution as a limit of a sequence of Lipschitz continuous solutions to the parabolic problem. It is proved that an admissible weak solution of the Cauchy problem is unique in the class BV.
Stability of a smooth flow in a Laval nozzle
Authors: Lar'kin Nikolaj , Wendland W. 
Published: August 2005

AbstractA boundary‐value problem for a non‐linear second‐order equation of mixed type in a cylindrical domain is considered. This problem simulates the development of small disturbances in a transonic flow of a chemical mixture in a Laval nozzle.The existence of a regular solution is proved with the help of a priori estimates for a corresponding linear problem and the contractive mapping theorem. The solution of the linear problem is constructed by the Galerkin method.
On a Galerkin‐averaging method for weakly non‐linear wave equations
Authors: Krol M. S. , Eckhaus W. 
Published: August 2005

AbstractSolutions of weakly non‐linear wave equations can be approximated using Galerkin's procedure combined with the averaging method. In this paper existence and uniqueness of solutions are proved in suitably chosen function spaces. Error‐estimates lead us to results on asymptotic validity of the approximations. Some applications are indicated.
Regular solutions of transmission and interaction problems for wave equations
Authors: Mehmeti Felix Ali , Meister E. 
Published: August 2005

AbstractConsider n bounded domains Ω ⊆ ℝ and elliptic formally symmetric differential operators A1 of second order on Ωi Choose any closed subspace V in \documentclass{article}\pagestyle{empty}\begin{document}$ \prod\limits_{i = 1}^n {L^2 \left({\Omega _i } \right)} $\end{document}, and extend (Ai)i=1,…,n by Friedrich's theorem to a self‐adjoint operator A with D(A1/2) = V (interaction operator). We give asymptotic estimates for the eigenvalues of A and consider wave equations with interaction.With this concept, we solve a large class of problems including interface problems and transmission problems on ramified spaces.25,32 We also treat non‐linear interaction, using a theorem of Minty29.
Stability and optimal control of thermomechanical processes with non‐convex free energies of Ginzburg–Landau type
Authors: Sprekels Jürgen , Brosowski B. 
Published: August 2005

AbstractIn this paper we study a coupled non‐linear system of partial differential equations that models the dynamics of structural phase transitions in a one‐dimensional non‐viscous and heat‐conducting solid. The corresponding Helmholtz free energy density is assumed in Ginzburg–Landau form; to allow for phase transitions and hysteresis phenomena, it is not assumed convex in the order parameter. It is shown that the solution of the system depends continuously upon the data, and we prove an existence result for an associated optimal control problem.
Remarks on exponential splines, in particular a contour integral representation of exponential B‐splines
Authors: Walz Guido , Brosowski B. 
Published: August 2005

AbstractIn the present paper we consider spline functions which are piecewise exponential sums of the form Σ αμeμx. Using the notation of Schumaker [10], we construct recursively computable B‐splines of this space, where we make use of a complex contour integral.Furthermore, it is shown that this definition of a B‐spline coincides in a certain sense with the ‘usual’ ones. which are based on the concept of generalized divided differences (e.g. [3, 12]).Finally, some additional properties of exponential B‐splines are presented, including a differential relation.
Global solutions of Yang–Mills–Higgs systems on four‐dimensional Minkowski space: II. Some properties of solutions
Authors: Łada A. 
Published: August 2005

AbstractThe paper concerns the properties of global solutions to the Cauchy problem of Yang–Mills–Higgs systems in the temporal gauge. The following properties are considered: global analyticity of solutions, an approximation property, conservation of the topological class of solutions, scattering of a part of the energy of solutions through a light cone.
Examples of embedded eigenvalues for the Dirichlet‐Laplacian in domains with infinite boundaries
Authors: Witsch Karl J. 
Published: August 2005

AbstractFor certain unbounded domains the Laplace operator with Dirichlet condition is shown to have an unbounded sequence of eigenvalues which are embedded into the essential spectrum. A typical example of such a domain is a locally perturbed cylinder with circular cross‐section whose diameter in some bounded subset is greater than at infinity.
The propagation problem and far‐field patterns in a stratified finite‐depth ocean
Authors: Gilbert R. P. , Xu Yongzhi 
Published: August 2005

AbstractIn this paper we investigate the direct problem associated with the scattering of ‘plane waves’ from an object submerged in an ocean of finite depth. An integral representation for the Dirichlet problem is found, from which a formula for the far‐field pattern evolves.A density theorem is established concerning the set of all far‐field patterns. This theorem is essential for the reconstruction of the submerged object, the ‘inverse’ problem [2], [4], [5].
Boundary value problems to a certain class of non‐linear diffusion equations
Authors: Nagasawa Takeyuki 
Published: August 2005

AbstractThe first initial‐boundary value problem and the free boundary of Stefan's type for a certain class of non‐linear diffusion equations which arises in plasma physics are considered. For the first initial‐boundary value problem, the global existence of a classical and its large‐time behaviour are discussed. The free‐boundary problem is studied by the reduction to the first initial‐boundary value problem.
The global existence of solutions to the equations of motion of a viscous gas with an artificial viscosity
Authors: Neustupa JiřÍ 
Published: August 2005

AbstractWe deal with the system of equations of motion of a viscous barotropic fluid. The system contains an artificial viscosity, which depends on the density ρ of the fluid and is identically equal to zero for ρ ϵ 〈0, ρ2〉 (where, ρ2 is a given positive number). If ρ2 is chosen sufficiently large, the system coincides with the Navier–Stokes equations and the equations of continuity if the density has values that actually appear in real flows. The velocity is assumed to be equal to zero on the boundary of the flow field and the body force is not taken into account. Initial conditions need not be ‘small enough’. Applying the method of discretization in time, the existence of a weak solution on an interval of an arbitarary (but finite) length is proved and an estimate of the energy character is derived.
Global existence of weak solutions for a system of non‐linear Boltzmann equations in semiconductor physics
Authors: Mustieles Francisco José 
Published: August 2005

AbstractIn this paper we give a proof of the global existence of weak solutions for the semiconductor Boltzmann equation. This equation rules the evolution of the distribution function of carriers in the kinetic model of semiconductors. The main tool for the proof consists of a recent compactness result on velocity averages of solutions of transport equations. This result needs a L2‐estimate of the electric field, which is obtained from the energy estimate, using the original regularization procedure of the problem, proposed in this paper.
An approximation of the thermal field in a continuous casting process of a thin metal layer
Authors: Comparini Elena , Manni Carla 
Published: August 2005

AbstractWe consider the problem of a phase change in a continuous casting process: molten bronze is poured on to a moving steel strip cooled from below, in order to solidify the bronze. An estimate of the width of the solidification zone, depending on the thickness of the strip and on the casting velocity, is obtained, neglecting conduction in the direction of the strip motion.
The problem of equivalence in statistical mechanics of equilibrium
Authors: Schröter J. , Wegener R. 
Published: August 2005

AbstractThe physical problem of the equivalence of certain partition function in statistical mechanics leads to the following mathematical problem: Under what conditions is the logarithm of a Laplace–Stieltjes transform of the so‐called microcanonical partition function equal to a Legendre transform of the logarithm of the latter? The conditions we shall formulate turn out to be physically reasonable.
Asymptotic completeness in optical scattering
Authors: Jochmann F. 
Published: August 2005

AbstractIn this paper time‐dependent methods are developed in order to prove the existence of the wave operators and asymptotic completeness in the scattering theory of electromagnetic waves in inhomogeneous media.The medium has a localized perturbation of the dielectric susceptibility. There are no regularity assumptions about the dielectric susceptibility.It is shown directly that the range of the wave operator is the complete continuous subspace, and not just the absolutely continuous subspace of the generator of the time evolution describing the perturbed wave propagation.
Local existence for solutions of fully non‐linear wave equations
Authors: Lesky Peter 
Published: August 2005

AbstractLet Ω be a domain in ℝn and let mϵ ℕ; be given. We study the initial‐boundary value problem for the equation

with a homogeneous Dirichlet boundary condition; here u is a scalar function, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar D_x^m u: = (\partial _x^\alpha u)_{|\alpha | \le m} $\end{document} and certain restrictions are made on F guaranteeing that energy estimates are possible. We prove the existence of a value of T>0 such that a unique classical solution u exists on [0, T]×Ω. Furthermore, we show that T → ∞ if the data tend to zero.
Exact solutions to the combined KdV and mKdV equation
Authors: Mohamad M. N. B. 
Published: August 2005

AbstractThis paper presents two different methods for the construction of exact solutions to the combined KdV and mKdV equation. The first method is a direct one based on a general form of solution to both the KdV and the modified KdV (mKdV) equations. The second method is a leading order analysis method. The method was devised by Jeffrey and Xu. Each of these methods is capable of solving the combined KdV and mKdV equation exactly.
Estimating ∇u by div u and curl u
Authors: Von Wahl Wolf 
Published: August 2005

AbstractIn this paper we obtain necessary and sufficient conditions for the validity of the estimate
magnified image
The constant c does not depend on u. u is a vector field with values in ℝ3. It is defined on a bounded set G of ℝ3 or an unbounded one, denoted by Ĝ. The boundary conditions are as follows: either the normal component of u vanishes or the tangential one does. Our conditions are expressed in terms of the Betti numbers of G or Ĝ.
An identification problem for a linear integrodifferential equation occurring in heat flow
Authors: Grasselli Maurizio 
Published: August 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 recovered by using an overdetermined set of data. A local existence theorem for small times and the continuous dependence of the solutions on the data are shown.
Stationary Boltzmann's equation with Maxwell's boundary conditions in a bounded domain
Authors: Palczewski Andrzej 
Published: August 2005

AbstractThe paper deals with the stationary Boltzmann equation in a bounded convex domain Ω. The boundary ∂Ω is assumed to be a piecewise algebraic variety of the C2‐class that fulfils Liapunov's conditions. On the boundary we impose the so‐called Maxwell boundary conditions, that is a convex combination of specular and diffusive reflections. The non‐linear Boltzmann equation is considered with additional volume and boundary source terms and it has been proved that for sufficiently small sources the problem possesses a unique solution in a properly chosen subspace of C(Ω × ℝ3). The proof is a refined version of the proof delivered by Guiraud for purely diffusive reflection.
New results for guided waves in heterogeneous elastic media
Authors: Joly Patrick , Weder Ricardo 
Published: August 2005

AbstractWe prove the existence of guided waves propagating with a velocity strictly larger than theS(shear) wave velocity at infinity in the case of unbounded elastic media invariant under translation in one space direction and asymptotically homogeneous at infinity.These waves correspond to the existence of eigenvalues embedded in the essential spectrum of the self‐adjoint elastic propagator.
On missing boundary conditions with unsteady incompressible Navier–Stokes flows
Authors: Hebeker F. K. , Wilde P. 
Published: August 2005

AbstractWe investigate an unsteady viscous flow problem where ‘good’ boundary conditions are available on part of the boundary only. This problem appears when the flow phenomena one is interested in are concentrated on part of the flow region and, for reasons of computational economy, are numerically computed in this subregion only. Assuming that outside of the subregion the flow is not subjected to any acceleration forces, we develop an (abstract) combined finite‐element/boundary element scheme to compute the flow approximately. This scheme leads to a proof of the existence of a weak solution of the corresponding Navier–Stokes problem as well.
Regularization of a non‐characteristic Cauchy problem for the heat equation
Authors: Hào Dinh Nho 
Published: August 2005

AbstractThe non‐characteristic Cauchy problem for the heat equation uxx(x,t) = u1(x,t), 0 ⩽ x ⩽ 1, − ∞ < t < ∞, u(0,t) = φ(t), ux(0, t) = ψ(t), − ∞ < t < ∞ is regularizèd when approximate expressions for φ and ψ are given. Properties of the exact solution are used to obtain an explicit stability estimate.
Interaction between two parallel tunnels
Authors: Ghaboussi Jamshid , Ranken Randall E. 
Published: August 2005

AbstractA series of finite element analyses were performed to study the behaviour of a system of two parallel and adjacent tunnels. Various sequences of excavation of the two tunnels and installation of tunnel liners have been simulated in the analyses. Influence of various parameters on the behaviour of the two parallel tunnels has been investigated. The important parameters considered in this study are: the width of the pillar separating the two tunnels; the tunnel depth; support condition; sequence of excavation; and, to some extent, the influence of plastic yielding in the medium surrounding the two tunnels.
Treatment of hourglass patterns in low order finite element codes
Authors: Kosloff Dan , Frazier Gerald A. 
Published: August 2005

AbstractNumerical codes which use a one‐point quadrature integration rule to calculate stiffness matrices for the 2‐D quadrilateral element and the 3‐D hexahedral element, produce matrices which are singular with respect to a number of displacement patterns, other than the rigid body patterns. In this paper an economical method is derived to remove this singularity and which also produces accurate flexural response. For rectilinear element geometry the method is equivalent to the incompatible model element of Wilson et al.7 For non‐rectilinear element geometry a slight modification of the scheme is required in order to assure that it passes the patch test. The method of this paper can also be used in finite difference codes which experience similar difficulties.
Geothermal heat extraction by water circulation through a large crack in dry hot rock mass
Authors: Bažant Zdeněk P. , Ohtsubo Hideomi 
Published: August 2005

AbstractOne proposed geothermal heat extraction scheme relies on water circulation in a large vertical crack created by hydraulic fracturing in a hot dry impermeable rock mass. Water flow, heat convection and crack opening widths are analysed by finite elements. Governing field equations of the problem are first set up rigorously and then various small terms are identified and neglected, retaining the effects of pressure gradient, buoyancy, velocity head (kinetic energy) and head loss due to viscous friction in the water flow equation, and the effects of heat convection in water and heat conduction in rock in the heat transfer equation. The finite element scheme for water flow is based on a variational principle that is typical for diffusion problems, and for heat transfer it is based on the method of least‐square residuals. The system of differential equations is highly non‐linear. The non‐linear terms and coefficients are treated in the fiaite element analysis as constant; the finite element analysisof, the steady‐state pressures, fluxes and temperatures is then iterated, evaluating all non‐linear terms and coefficients on the basis of the solution obtained in the previous iteration. Numerically calculated fields at various times after the start ofcooling are presented. They indicate some features favourable for the geothermal scheme, such as formation of eddy currents, and downward flux of water toward hotter rock. However, other important questions would have to be solved to gain full understanding, of this proposed geothermal scheme.
Consolidation due to shear loads distributed over a rectangular area
Authors: Shanker N. Babu , Sarma K. S. , Ratnam M. V. 
Published: August 2005

AbstractThe paper presents an analytical study of the consolidation of a semi‐infinite clay layer subjected to a shear load distributed over a rectangular area. Biot's theory is made use of, along with the three displacement functions suggested by Verruijt. A complex Fourier and Laplace transformation technique enables the solution to be obtained in terms of non‐dimensional parameters. Settlements and pore pressures under the loaded area are evaluated for two types of surface drainage conditions. Extension of the solutions to point loads is also suggested. The Mandel–Cryer effect is seen in the behaviour of the pore pressure.
A method to estimate the degree of consolidation of a non‐homogeneous clay layer
Authors: Ly Binh‐Le 
Published: August 2005

AbstractA method is derived to estimate the degree of consolidation of a saturated, non‐homogeneous clay layer. In this method, the diffusion equation govering the dissipation of pore water pressure is transformed so that the pore water pressure can be expressed by a Fourier series. The Fourier coefficients are then evaluated along the trajectory of the diffusion process. The Fourier series does not converge point‐wise to the pore water pressure; instead, it converges to the pore water pressure in the mean., The Fourier series can be used to estimate the degree of consolidation, because, by Schwartz's inequality, convergence in the mean implies convergence in the degree of consolidation.
Effects of restricted flow at the surface of saturated clay
Authors: Deresiewicz H. 
Published: August 2005

AbstractThe deflection of, and the pore pressure at, the surface of a saturated clay mass are computed by modelling the mass mathematically as a consolidationg half‐space. Specifically, attention is focused on the effect of a surface cover which impedes, though does not entirely prevent, the flow of the pore water. A number of results of interest are reported, generalizing work reported earlier by McNamee and Gibson8.
Dynamic stiffness for rectangular rigid foundations on a semi‐infinite elastic medium
Authors: Kitamura Yasutoshi , Sakurai Shunsuke 
Published: August 2005

AbstractThe present paper deals with the dynamic steady‐state force‐displacement relationships (complex stiffness) for rectangular rigid foundations resting on a semi‐infinite medium, consisting of homogenous, isotropic, linear elastic materials. The foundations are considered to be excited under harmonic vertical and rocking vibration. This gives mixed boundary value problems which cannot be easily solved by analytical approaches. Therefore, a numerical method is proposed here. The method is based on quite, simple equations, and is straightforward in computation, compared with other methods. Although the proposed method gives just approximate solutions, it is satisfactory for engineering practices, and the soluations become highly accurate for a small value of ωB/Vs. The results obtained by the proposed method are compared with those of other methods to evaluate the accuracy of the results. The effects of length/width ratio and the area of the contact plane of the foundations are also discussed.
Discrete element analysis of pile instability
Authors: Smith Ian M. 
Published: August 2005

AbstractRecently, instability of slender piles during installation has been analysed as a non‐conservative buckling process. For these results to be of potential use in practice, simple procedures are necessary whereby piles of arbitrary cross‐section installed in ground with arbitrarily varying properties can be treated. This paper lists discrete element matrices which enable the prediction of the onset of instability in piles assuming conservative or non‐conservative ground resistance. The same matrices can then be used to incorporate effects of incipient instability in driveability analyses.
Isotropic yield surfaces in three dimensions for use in soil mechanics
Authors: Van Eekelen H. A. M. 
Published: August 2005

AbstractWhen using numerical methods in soil mechanics, one often needs to define a yield surface in three‐dimensional principal‐stress space. A special class of yield surfaces, given by J = (p+a)α(1−β sin 3ν)n, where ν is the Lode angle, is considered from the point of view of convexity and agreement with experimental data. Some recently proposed yield functions which belong to this class are compared. It is shown that the model with n = −0.229 is optimal as regards convexity, and can give reasonable agreement with the data.