摘要:

AbstractWe consider the scattering of plane, time‐harmonic electromagnetic waves by a perfect conductor D. We first show that the set ℱλconsisting of the span of a fixed linear combination of the electric and magnetic far‐field patterns is dense in the space of square‐integrable tangential vector fields defined on the unit sphere for all values of the wave number k ≠ 0 provided that Im k ≥0. We next consider the affine hull

ISSN:0170-4214    

DOI:10.1002/mma.1670150102

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractSufficient conditions are obtained for the linear stability of the positive equilibrium of the neutral systemin terms of the parameters of the system. The case n=2 is considered in detail and the general case is discussed briefly.

ISSN:0170-4214    

DOI:10.1002/mma.1670150103

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractWe examine the numerical approximation of the integral equation (λ −K)u=f, whereKis the double layer (harmonic) potential operator on a closed polyhedral surface in ℝ3and λ, ∣λ∣≥1, is a complex constant. The solution is approximated by Galerkin's method, which is based on piecewise polynomials of arbitrary degree on graded triangulations. By utilizing spline spaces which are modified in that the trial functions vanish on some of the triangles closest to the vertices and edges, we investigate the stability of this method inL2. Furthermore, the use of suitably graded meshes leads to the same quasioptimal error estimates as in the case of a sm

ISSN:0170-4214    

DOI:10.1002/mma.1670150104

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractWe consider first and second‐order implicit time stepping procedures for the non‐stationary Stokes equations in bounded domains of ℝ3. Using energy estimates we prove the optimal convergence properties in the Sobolev spacesHm(G)(m = 0, 1, 2) uniformly in time, provided that the Stokes solution has a certain degree of regularity. Here in the case of the second‐order scheme (method of Crank–Nicholson) the Stokes solution has to satisfy a non‐local compatibility condition at the initial timet= O, which can be satisfied by a special initial c

ISSN:0170-4214    

DOI:10.1002/mma.1670150105

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractGiven self‐adjoint operatorsHj, on Hilbert spaces ℋ︁j,j= 0,l, andJ∈ ℬ︁ (ℋ︁0, ℋ︁1) (where ℬ︁ (ℋ︁0ℋ︁1) denotes the set of bounded linear operators from ℋ︁0to ℋ︁1), define the wave operatorswhereP0is the projection onto the subspace for absolute continuity for H0. We use (i) to study the scattering problem associated with a pair of equations each of the formwhereLis a positive, self‐adjoint operator on a Hilbert spaceX,mis a positive integer and the αjare distinct positive constants. Methods patterned after those of Kato are used to study two equations (that is forL=L0andL=Ll) each of the form (ii). We show that they are equivalent to equations of the formwhere each Ĥkis a self‐adjoint operator on an associated Hilbert space ℋ︁k. Now suppose∼he‐wave operatorsW±,(L1L0) exist and are complete. Then we can find aJ∈ ℬ︁(H1H0) such thatW+(Ĥl, Ĥ0,J) exists. In the case whereLoandL1have the same domain, ℋ︁1and ℋ︁0are equal as vector spaces, and under certain conditions (on Li,i= 0, 1) ℋ︁0and ℋ︁1have equivalent norms. Assuming these conditions, letJ'∈ ℬ︁(ℋ︁1' ℋ︁0) be the identity map. We show t

ISSN:0170-4214    

DOI:10.1002/mma.1670150106

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670150101

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY