摘要:

AbstractThe determination of the figure of the earth is considered as a local free boundary value problem of potential theory. In theC1,ε‐topology local existence is proved by means of Legendre transforms. This method also provides an elementary argument for the regularity of the solutio

ISSN:0170-4214    

DOI:10.1002/mma.1670080102

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractIn this paper, asymptotic expansions with respect to small Reynolds numbers are proved for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid past a single plane wall. The flow problem is modelled by a certain boundary value problem for the stationary, nonlinear Navier‐Stokes equations. The coefficients of these expansions are the solutions of various, linear Stokes problems which can be constructed by single layer potentials and corresponding boundary integral equations on the boundary surface of the particle. Furthermore, some asymptotic estimates at small Reynolds numbers are presented for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid between two parallel, plane walls and in an infinitely long, rectilinear cylinder of arbitrary cross section.In the case of the flow problem with a single plane wall, the paper is based on a thesis, which the author has written under the guidance of Professor Dr. Wolfgang L. Wendlan

ISSN:0170-4214    

DOI:10.1002/mma.1670080103

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA mixed problem imitating the Cauchy problem for the linearized shallow water equations is considered. This problem is also a mixed problem with perfectly absorbing conditions (cp. [1], [3]). An exact formula for the conditions has been given.

ISSN:0170-4214    

DOI:10.1002/mma.1670080104

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

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.

ISSN:0170-4214    

DOI:10.1002/mma.1670080105

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractWe treat the time‐harmonic Maxwell equations with the boundary condition (ν,E) = (ν,H) = 0 in an exterior multiply connected domain. A uniqueness result by Yee for the case of a simply connected domain is extended to multiply connected domains and existence is obtained by a boundary integral equation appro

ISSN:0170-4214    

DOI:10.1002/mma.1670080106

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractRecently N. Korevaar developed a method of proving that solutions to elliptic and parabolic boundary value problems on convex domains ω ⊂Rnare convex functions. He introduced a concavity functionand used the classical maximum principle to prove thatC⩾ 0 on ω × ω, i.e. thatuis convex. Both he and independently L. Caffarelli and J. Spruck applied this method successfully to various boundary value problems. In this note we weaken the assumptions of their theorems and obtain some interesting new applications which are not covered by their previous results [

ISSN:0170-4214    

DOI:10.1002/mma.1670080107

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

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.

ISSN:0170-4214    

DOI:10.1002/mma.1670080108

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

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 metho

ISSN:0170-4214    

DOI:10.1002/mma.1670080109

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractWe consider the Dirichlet problem for the reduced wave equation ΔUx+x2Ux= 0 in a two‐dimensional exterior domain with boundaryC, whereCconsists of a finite number of smooth closed curvesC1,…,Cm. The question of interest is the behavior ofUxas ϰ → 0. We show thatUconverges to the solution of the corresponding exterior Dirichlet problem of potential theory if the boundary data converge to a limit uniformly onC.This generalizes a well‐known result of R. C. MacCamy for the

ISSN:0170-4214    

DOI:10.1002/mma.1670080110

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

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 rep

ISSN:0170-4214    

DOI:10.1002/mma.1670080111

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY