摘要:

AbstractWe consider a domain Ω in ℝnof the form Ω = ℝl× Ω′ with bounded Ω′ ⊂ ℝn−l. In Ω we study the Dirichlet initial and boundary value problem for the equation ∂ t2u+ [(− ∂ 12−… − ∂ l2)m+ (− ∂ l+12−… − ∂ n2)m]u=fe−iωt. We show that resonances can occur if 2m≥l. In particular, the amplitude ofumay increase liketα(α rational, 0<α<1) or like intast∞∞. Furthermore, we prove

ISSN:0170-4214    

DOI:10.1002/mma.1670110601

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIn this article, we introduce and study a family of artificial boundary conditions for the diffusion equation. These conditions are local in time and non‐local in space. We describe the principle of the approximation, show that the corresponding approximate problems are mathematically well‐posed and give convergence results, as well as error estimates, of the approximate solution to the exact

ISSN:0170-4214    

DOI:10.1002/mma.1670110602

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractConsider a cylindrical pipe twisted by terminal couples. For a large twist θ, the elastic‐plastic stress function, Ψ (·,θ), is shown to be the positive in the interior of the pipe, an increasing function of θ and converging to the completely plastic stress function,\documentclass{article}\pagestyle{empty}\begin{document}$ \bar \Psi \left(\cdot \right) $\end{document}(·), as θ→∞. A geometric procedure for constructing Ψ(·) has been developed to provide qualitative information. The main result states that\documentclass{article}\pagestyle{empty}\begin{document}$ \psi \left({\cdot,\theta} \right) = \bar \Psi \left(\cdot \right) $\end{document}on the cross‐sectional boundary of the pipe, if θ is greater than or equal to a certain critical value, In addition, an example has been constructed to give ad

ISSN:0170-4214    

DOI:10.1002/mma.1670110603

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe far‐field operator for an exterior boundary value problem for the Helmholtz equation maps the boundary data onto the far‐field pattern of the solution. This paper computes theL2‐adjoint of this operator for various choices of boundary conditions. In scattering theory the boundary data are given by the traces of plane waves. We characterize the closure of the span of the images of these plane waves under the far field operator.Finally, the results are extended to more general topologies including Sobolev and Hölder

ISSN:0170-4214    

DOI:10.1002/mma.1670110604

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe surface gradients of some of the most important boundary integral operators for the time‐harmonic Helmholtz and Maxwell equations are computed. These results are used to give new and elementary proofs of the continuity properties of these boundary operators in Sobolev and Hölder spaces of arbitrary ord

ISSN:0170-4214    

DOI:10.1002/mma.1670110605

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractWe consider several elliptic boundary value problems for which there is an overspecification of data on the boundary of the domain. After reformulating the problems in an equivalent integral form, we use the alternate integral formulation to deduce that if a solution exists, then the domain must be anN‐ball. Various Green's functions and classical boundary value problems of second, fourth and higher order are included among the problems considered her

ISSN:0170-4214    

DOI:10.1002/mma.1670110606

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIn the present paper we consider spline functions which are piecewise exponential sums of the form Σ μ=1mαμeμx. 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 diffe

ISSN:0170-4214    

DOI:10.1002/mma.1670110607

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY