摘要:

AbstractThe aim of this paper is to prove the existence and uniqueness of local solutions of some initial boundary value problems for the Euler equations of an incompressible fluid in a bounded domain Ω ⊂R2with corners. We consider two cases of a nonvanishing normal component of velocity on the boundary. In three‐dimensional case such problems have been considered in papers [12], [13], [14]. Similar problems in domains without corners have been considered in [2]–[6], [11]. In this paper the relation between the maximal corner angle of the boundary and the smoothness of the solutions is shown. The paper consists of four sections. In section 1 two initial boundary value problems for the Euler equations are formulated. In section 2 the existence and uniqueness of solutions of the Laplace equation in twodimensional domain with corners for the Dirichlet and Neumann problems is proved in the Sobolev spaces. In sections 3 and 4 we prove the existence and uniqueness of solutions of problems formulated in section 1, using the method of successive approxim

ISSN:0170-4214    

DOI:10.1002/mma.1670060102

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA simplified Fokker‐Planck equation of statistical plasma physics is mathematically investigated. For the Cauchy problem a constructive approximation method is introduced. This procedure yields a sequence (fn) of approximate densities, uniformly converging to the problem's global classical solution with linear convergence velocit

ISSN:0170-4214    

DOI:10.1002/mma.1670060103

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractWe consider the evolution equationu'=Au+Nuu(0) = ϕuis a function on a real interval [0,T] with values in a Hilbert spaceH, Ais a linear operator inHgenerating a continuous semigroupeAtandNis a nonlinear operator inH.We show that1Existence of the exact solution implies existence of the Faedo‐Galerkin Approximations.2Existence of the Faedo‐Galerkin Approximations implies existence of the exact solution.3Uniform convergence of the Faedo‐Galerkin Approximations to the exact solution.The Paper consists of two parts. In the first five sections we require thatApossesses a complete orthonormal system of eigenfunctions, in section 6 we drop this requi

ISSN:0170-4214    

DOI:10.1002/mma.1670060104

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA string fixed at both endsAandB, can oscillate in a plane which there is a fixed point obstacle, placed in the middle of the lineAB. The string is initially at rest with a prescribed shape, symmetric with respect to the normal mid‐plane of the segmentAB. Using results established before [9] we find new periodic motion

ISSN:0170-4214    

DOI:10.1002/mma.1670060105

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA linear equation for a particle steady‐state transport process in a homogeneous slab of finite thickness with boundary conditions of general type is derived. This equation differs from the well‐known integral equation for no‐reentry boundary conditions because of the presence of a per‐turbance linear operator which describes the effect of the re‐emission of the particles incident at the wall. The properties of the resulting operator are investigated. The dependence of the first positive eigenvalue on physical parameters is studies in detail. The results obtained are enough to discuss the existence of a critical strictly positive solution of the physical problems which motivated this

ISSN:0170-4214    

DOI:10.1002/mma.1670060106

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractWe formulate the roller contact problem in terms of variational inequality with certain pseudodifferentional operator, and discuss a finite element technique for its numerical solution.

ISSN:0170-4214    

DOI:10.1002/mma.1670060107

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThe present paper is concerned with the study of retarded differential equations inn‐space, which satisfy some monotonicity properties. Sufficient conditions are given guaranteeing that solutions are contained in the probability (n– 1)‐simplex. Existence and uniqueness of constant solutions are proved. It is also shown that every solution converges to a constant a

ISSN:0170-4214    

DOI:10.1002/mma.1670060108

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractWe discuss the asymptotic behaviour of acoustic and electromagnetic waves, generated by given time‐harmonic exterior forces with frequency ω, in the unbounded region between the parallel planesX3= 0 andX3= 1, and show that the principle of limiting amplitude is violated if ω = πn(n= 1, 2,…). For these values of the frequency, forces with compact support can be chosen such that the amplitudes of the waves increase with a logarithmic rate

ISSN:0170-4214    

DOI:10.1002/mma.1670060109

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThe plane transmission problem of the Helmholtz equation for quadrants is characterized by a one‐dimensional singular integral equation, which refers to the Fourier transform of the normal derivative of the solution along thex‐axis. It is derived by solving the transmission problem for the upper and the lower half‐plane involving a Neumann condition aty= 0. This is done by a two‐dimensional Laplace transform technique. The inverse Laplace transform with respect to the second cartesian coordinate and the restriction of this one toy= 0 then lead to the integral equation. Thereby the transmission conditions of the original problem aty= 0 have to be taken into account. The resulting integral equation is of generalized Wiener‐Hopf‐type. It is solved via the contraction theorem imposing restricting conditions on the w

ISSN:0170-4214    

DOI:10.1002/mma.1670060110

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670060111

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY