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  • Atomic, Molecular and Optical Physics  (301)
  • Mathematics and Statistics  (107)
  • Wiley-Blackwell  (408)
  • 1990-1994  (408)
  • 1993  (408)
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  • Wiley-Blackwell  (408)
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  • 1990-1994  (408)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    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.1670160101
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  • 2
    Electronic Resource
    Electronic Resource
    Behaviour of mushy regions under the action of a volumetric heat source (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 35-47 
    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 solutions to Stefan problems in spatial dimensions N ≥ 1. We find the necessary conditions on the heat source for the appearance of a ‘mushy region’ (i.e. a region where the temperature coincides identically with the temperature of the change of phase) inside a purely liquid (or solid) phase. For sources depending on energy such conditions are connected only with the local behaviour of the source near the energy level corresponding to the beginning of the change or phase. Both weak and smooth solutions are considered; in the latter case the behaviour of the solution at the free boundary is investigated in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160104
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  • 3
    Electronic Resource
    Electronic Resource
    On the asymptotic growth of the solutions of the vlasov-poisson system (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 75-85 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show the global existence of classical solutions of the Vlasov-Poisson system and improve the known growth estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160202
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  • 4
    Electronic Resource
    Electronic Resource
    High-frequency asymptotics in inverse scattering by ellipsoids (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 1-12 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A triaxial ellipsoid of unknown position, size and orientation is located somewhere in space. High-frequency asymptotics for the scattering amplitude and the sojourn time for the travelling of a high-frequency acoustic plane wave are utilized to determine the position of a supporting plane for the ellipsoid. We describe a method that identifies the coordinates of the centre, the three semiaxes, and the three angles of the ellipsoid from the knowledge of nine sojourn times corresponding to nine directions of excitation. The method is independent of boundary conditions, it is applicable to any restricted non-zero-measure angle of observation, and leads to numerics that avoid elliptic integrals. A priori information about the location of the ellipsoid reduces the number of measurements to six, while the corresponding algorithm demands the solution of a linear system and the inversion of a dyadic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160102
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  • 5
    Electronic Resource
    Electronic Resource
    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    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.1670160201
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  • 6
    Electronic Resource
    Electronic Resource
    Schauder estimates for boundary layer potentials (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 877-894 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Boundary layer potentials with Hölder-continuous densities are widely used for representing solutions of boundary value problems for certain partial differential equations. These potentials are of the type with |ρ| odd and a density λ of class Ck+α. This paper presents a self-contained exposition of the fact that the potential v may be continued as Ck+α-functions onto G and ∝n\G respectively (together with estimates for the Hölder-norms) under the least possible regularity assumption for the boundary ∂G: it has to be of class Ck+1+α.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161204
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  • 7
    Electronic Resource
    Electronic Resource
    A non-isentropic Euler-Poisson model for a collisionless plasma (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 409-442 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse transonic solutions of the one-dimensional Euler-Poisson model for a collisionless gas of charged particles in the non-isentropic steady-state case. The model consists of the conservation of mass, momentum and energy equations. The electric field is modelled self-consistently (Coulomb field). Boundary conditions on the particle density and particle temperature are imposed.The analysis is based on representing solutions piecewise as orbits in the particle-density-electric-field phase plane and connecting the orbit segments by the jump and entropy conditions.We characterize the set of all solutions of the Euler-Poisson problem. In particular, we show that, depending upon the length of the interval on which the boundary value problem is posed, fully subsonic, one-shock and (in certain cases) two-shock transonic and smooth transonic solutions exist. Also, numerical computations illustrating the structure of the solutions are reported.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160603
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  • 8
    Electronic Resource
    Electronic Resource
    Resonance phenomena in a semi-infinite string with a periodic end (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 501-531 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in a semi-infinite string under the assumption that the material properties depend p-period-ically on the space variable outside a sufficiently large interval [0, a]. The spectrum of the self-adjoint extension A of the spatial part of the differential operator consists of a finite or countable number of bands and a (possibly empty) discrete set of eigenvalues located in the gaps of the continuous spectrum. We show that resonances of order t or t½, respectively, occur if either ω2 is an eigenvalue of A or (i) ω2 is a boundary point of the continuous spectrum of A and (ii) the corresponding time-independent homogeneous problem has a non-trivial solution which is p-periodic or p-semiperiodic for x 〉 a (‘standing wave’).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160704
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  • 9
    Electronic Resource
    Electronic Resource
    Relative entropy maximization and directed diffusion equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 545-554 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Motivated by the concept of maximum entropy methods in signal and image processing, we introduce and discuss a class of ‘directed diffusion equations’ with suitable boundary conditions. The paradigmatic ‘directed diffusion equation’ is The relative entropy \documentclass{article}\pagestyle{empty}\begin{document}$ Sb[f](t): = - \int_\Omega {f(t,x)} \;\ln \;(f(t,x)/b(x))dx $\end{document} is rapidly increasing along solution trajectories of (i). This suggests that solving (i) will yield efficient procedures for entropy maximization. We also discuss the asymptotic behavior of solutions of (i) - this is readily done because (i) has a large family of Ljapunov functionals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160803
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  • 10
    Electronic Resource
    Electronic Resource
    A normal crack in an elastic half-space with stress-free surface (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 563-579 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of an elastic half-space with stress-free surface and a crack of arbitrary shape with prescribed displacements or tractions is reduced to an equivalent system of integral equations on the crack. For a pressurized crack in a plane perpendicular to the free surface, a scalar integral equation is derived. In properly chosen function spaces, unique solvability of the integral equation and regularity of solutions for regular data are proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160805
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