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  • 1
    Electronic Resource
    Electronic Resource
    Eine Integralgleichungsmethode für akustische Reflexionsprobleme an lokal gestörten Ebenen (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 128-144 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the reflection of acoustic waves at an unbounded surface which coincides with a plane outside a sufficiently large sphere. We prove uniqueness and existence theorems for the corresponding boundary value problems for the reduced wave equation with Dirichlet and Neumann data by employing integral equation methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030111
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Lösungen der poissongleichung und harmonische vektorfelder in unbeschränkten gebieten (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 233-255 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the first part of this paper we consider generalised solutions of the Poisson equation Δ U = F in open subsets of Rn(n ≥ 3) with Dirichlet or Neumann boundary data. We prove existence and uniqueness theorems, not only for the corresponding interior and exterior problems, but also for domains with boundaries extending to infinity. In the second part we discuss generalised harmonic fields in open subsets of R3 with vanishing Dirichlet or Neumann boundary condition.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050117
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Ein resonanzphänomen in der theorie akustischer und elektromagnetischer wellenHerrn Professor Karl Nickel zum 60. Geburtstag am 9. 2. 1984 gewidmet (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 104-128 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We 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 planes X3 = 0 and X3 = 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 as t → ∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060109
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Regularity theorems for Maxwell's equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 523-536 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Methods using the theory of distributions and Hilbert space operators have been very powerful in the past to achieve uniqueness and existence results for Maxwell's equations. In this paper conditions are given when such abstract “Hilbert space”-solutions represent differentiable “regular” functions which satisfy Maxwell's equations, boundary conditions, and transmission conditions in the classical sense.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030137
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Akustische wellen in Gebieten, die von zwei lokal gestorten parallelen ebenen begrenzt sind (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 397-414 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider acoustic waves in domains with boundaries, coinciding with two parallel planes outside a sufficiently large sphere. Several results on spectral properties of the Laplace operator in such domains are derived and used to prove uniqueness and existence of a solution of the Dirichlet boundary value problem for the reduced wave equation under additional restrictions. In particular, a class of domains is described for which no eigenvalues are present.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040125
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    A local compactness theorem for Maxwell's equations (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 12-25 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper gives a proof, valid for a large class of bounded domains, of the following compactness statements: Let G be a bounded domain, β be a tensor-valued function on G satisfying certain restrictions, and let {n} be a sequence of vector-valued functions on G where the L2-norms of {n}, {curl n}, and {div(β n)} are bounded, and where all n either satisfy x n = 0 or (β Fn) = 0 at the boundary ∂G of G ( = normal to ∂G): then {n} has a L2-convergent subsequence. The first boundary condition is satisfied by electric fields, the second one by magnetic fields at a perfectly conducting boundary ∂G if β is interpreted as electric dielectricity ∊ or as magnetic permeability μ, respectively.These compactness statements are essential for the application of abstract scattering theory to the boundary value problem for Maxwell's equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020103
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    Paper (German National Licenses)
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