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  • Wiley-Blackwell  (8)
  • 1
    Electronic Resource
    Electronic Resource
    Nonselfadjoint operators in diffraction and scattering (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 327-346 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020307
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  • 2
    Electronic Resource
    Electronic Resource
    On uniqueness of Neumann-Tricomi problem in R2 (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 168-177 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the equation of mixed type (k(y) ⋛ 0 whenever y ⋛ 0) in a region G which is bounded by the curves: A piecewise smooth curve Γ lying in the half-plane y 〉 0 which intersects the line y = 0 at the points A(-1, 0) and B(0, 0). For y 〈 0 by a piecewise smooth curve Γ through A which meets the characteristic of (1) issued from B at the point P and the curve Γ which consists of the portion PB of the characteristic through B. We obtain sufficient conditions for the uniqueness of the solution of the problem L[u] = f, dnu: = k(y)uxdy - uydx|γ0 = = Ψ(s) for a “general” function k(y), when r(x, y) is not necessarily zero and Γ1 is of a more general form then in the papers of V. P. Egorov [6], [7].
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020204
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  • 3
    Electronic Resource
    Electronic Resource
    The two-dimensional, linear, orthotropic plate: The traction problem (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 102-116 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In [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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080108
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  • 4
    Electronic Resource
    Electronic Resource
    The propagation problem and far-field patterns in a stratified finite-depth ocean (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 199-208 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we investigate the direct problem associated with the scattering of ‘plane waves’ from an object submerged in an ocean of finite depth. An integral representation for the Dirichlet problem is found, from which a formula for the far-field pattern evolves.A density theorem is established concerning the set of all far-field patterns. This theorem is essential for the reconstruction of the submerged object, the ‘inverse’ problem [2], [4], [5].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670120303
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  • 5
    Electronic Resource
    Electronic Resource
    A solution to the equations of shell theory (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 341-363 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the Vekua-Dikmen formulation of the equations of shell theory as a heirarchy are presented as a hypercomplex system. Using the function theory associated with this algebra the torsion problem is solved as an integral representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670120405
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  • 6
    Electronic Resource
    Electronic Resource
    Dense sets and the projection theorem for acoustic harmonic waves in a homogeneous finite depth ocean (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 69-76 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The scattering of a ‘plane wave’ off a submerged body situated in an ocean of finite depth is investigated. The index of refraction is considered to be depth-independent. It is shown that the far field is not unique; hence, the problem of determining the shape of an object from its far field is not well-posed. If solutions are sought among a restricted class of problems the ‘dense set’ property implies that the problem can be made well-posed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670120105
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  • 7
    Electronic Resource
    Electronic Resource
    Existence and uniqueness for an equation of mixed type in a rectangle (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 307-316 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A boundary value problem is considered for an equation of mixed type in a rectangle. An energy method is used to prove uniqueness for appropriate boundary conditions. Similar considerations for the adjoint problem allow one to prove the existence of a generalized solution to the problem. It is also shown that the energy method leads naturally to a finite element method. The method is described for a special case and convergence is shown for the resulting numerical procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040121
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  • 8
    Electronic Resource
    Electronic Resource
    Some remarks on Newton-Sabatier methods (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 43-63 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown how Newton-Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovič-Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110103
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