摘要:

AbstractIn References 4 and 5, the author studied the geometric form of the free boundary Γ of an annular domain Ω, characterized by the Bernoulli condition that |∇U|=1 on Γ, whereUis the capacity potential in Ω. It was shown, for example, that Γ has at most as many ν‐extrema (for a given direction ν) or inflection points as the other boundary component Γ* of Ω, which is assumed given. Our purpose here is to extend the results in References 4 and 5 (wherever possible) to multiply connected regions for which some boundary components are given and others are free boundaries characterized by the Bernoulli condition. We present both positive results and cou

ISSN:0170-4214    

DOI:10.1002/mma.1670100102

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractA study is performed of transport equations on arbitrary three‐dimensional domains with boundary conditions of reverse reflection type. The existence of the dominant eigenvalue of the criticality problem is proved and its independence of the functional setting and its continuous dependence on a variety of data are established. The corresponding time‐dependent problem is shown to be well‐posed, also for a conservative boundary. The relationship between the criticality and the time‐dependent problem is given exp

ISSN:0170-4214    

DOI:10.1002/mma.1670100103

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractThe Föppl‐Hencky theory of small finite deflections has been applied to the study of axisymmetric deformations of annular membranes by various authors. The mathematical problem of uniqueness of tensile solutions for the corresponding non‐linear boundary value problems in the full range of physically meaningful boundary data was solved only recently.3, 4In this paper, a new integral equation technique of solution is developed which yields the existence of tensile solutions for a parameter range of the boundary data where previous investigations on this matter had not been successful. It is shown that tensile solutions no longer exist, when sufficiently large positive radial displacements are prescribed at the inner edge of the ann

ISSN:0170-4214    

DOI:10.1002/mma.1670100104

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractFor certain types of semilinear partial differential equations in a cylindrical domain small bounded solutions are known to lie on a so‐called centre manifold of finite dimension. In this paper we prove the result for quasilinear partial differential equations of elliptic and parabolic type.Possible applications include free surface waves and problems in non‐linear elasticity. Here we investigate, pars pro toto, the stationary inviscid potential flow in a channel with a free surface and an obstacle at the bot

ISSN:0170-4214    

DOI:10.1002/mma.1670100105

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractA method is described for studying analytic boundary problems for the Laplace equation in a simplyconnected domainDof the plane. The aim is ultimately to obtain solutions in closed form whenDis bounded by a simple analytic curveCwith Schwarz functionG. The basis for the procedure is that a functionalFof the incompletely known boundary Cauchy data determines the solution and is analytic inD, and that there exists a further integral relation between these data and the analytic functionG. Elimination of the unknown data from the latter relation by using the former leads to an integral onCthat relatesFto prescribed data and which, in some cases, may be solved forFinD. Some necessary properties ofGare derived; in particular, it is shown thatCmust be a circle ifGis analytic inDexcept for a single, simple pole (Theorem 1), or if a certain integral that appears prominently in this work is analytic throughoutD(Theorem 2). The Dirichlet problem is treated in some detail. IfCis a circle, a representation for the solution is obtained that is equivalent to one given by P. J Davis, and to the Poisson integral. WhenGis meromorphic inDandCis not a circle, Theorem 2 implies that the Davis result is not applicable, and the problem is reduced to that of solving Schröder's functional equation. Integral equations forFare obtained whenCis an ellipse andGis multivalued inD. Other linear boundary value problems that can be handled are noted. A class of non‐linear Riemann‐Hilbert problems is described and studied briefly. For all these problems, closed solutions have been obtained whenCis a circle; it is not clear whether closed solutions for other forms ofCcan be found without the explicit use of conformal mapping techniques. Finally, some possible generalizations to different equations and more complicated geometries are menti

ISSN:0170-4214    

DOI:10.1002/mma.1670100106

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670100101

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY