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  • Mathematics and Statistics  (520)
  • Wiley-Blackwell  (520)
  • Blackwell Publishing Ltd
  • Periodicals Archive Online (PAO)
  • 1990-1994  (520)
Collection
Keywords
Publisher
  • Wiley-Blackwell  (520)
  • Blackwell Publishing Ltd
  • Periodicals Archive Online (PAO)
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    Some decomposition theorems and their application to non-linear potential theory and Hodge theory (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 35-52 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers Dirichlet (or Neumann type) boundary value problems of generalized potential theory \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm d}\alpha = f,\;\delta \varepsilon \left(\alpha \right) = g\,{\rm in}\,M, $$\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$$ \alpha = 0\,{\rm on}\,\partial M $$\end{document} on Lipschitz manifolds with boundary. Here ∊ denotes a permissible non-linearity. The existence theory is developed in the framework of monotone operators. The approach covers a variety of applications including fluid dynamics and electro- and magneto-statics. Only fairly weak regularity assumptions are required (e.g. Lipschitz boundary, L∞-coefficients). As a by-product we obtain a non-linear Hodge theorem generalizing a result by L. M. Sibner and R. J. Sibner (‘A non-linear Hodge-DeRham theorem’, Acta Math., 125, 57-73 (1970)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670120103
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  • 2
    Electronic Resource
    Electronic Resource
    Time-invariant uniqueness for reacting viscous fluids near chemical equilibrium (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 137-141 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A system of equations is investigated which models a reacting mixture of viscous fluids acted upon by an external body force. Through logarithmic convexity arguments the solution is shown to be unique when either the initial or the final data are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130204
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  • 3
    Electronic Resource
    Electronic Resource
    Remarks on the wave front of polarization: Polarized solutions for the evolution three-dimensional Lame system (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 181-188 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Some remarks complementary to the work of N. Dencker in [1] concerning the wave front of polarization are given. The theorem due to N. Dencker about the propagation of a wave front of polarization is applied to solutions for the evolution of the three-dimensional Lame system. The propagation of polarized solutions is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130208
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  • 4
    Electronic Resource
    Electronic Resource
    On a contact problem for a system of parabolic equations in the thermal conductivity of electric machines: II (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 249-261 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The non-linear contact problem for the parabolic system of second order in the sense of Pietrovski, which is the generalization of the problem considered in Part I (preceding paper), is formulated. The matrix of fundamental solutions for parabolic systems of second order with coefficients containing unknown functions and their first-order derivatives is constructed and used to reduce the problem to the equivalent system of integral equations which is then reduced to a system of Volterra type of the second kind. The existence of the solution of the system obtained is proved by using the Schauder fixed-point theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130306
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  • 5
    Electronic Resource
    Electronic Resource
    The scattering of electromagnetic waves by a perfectly conducting infinite cylinder (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 503-518 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the scattering of a plane time-harmonic electromagnetic wave by a perfectly conducting infinite cylinder with axis in the direction k, where k is the unit vector along the z axis. Suppose the incident wave propagates in a direction perpendicular to the cylinder. For a given observation angle θ, let FD(θ, α)k be the far-field pattern of the electric field corresponding to an incident wave with direction angle α polarized perpendicular to the axis and let FN(θ; α)k be the far-field pattern of the magnetic field corresponding to an incident wave with direction angle α polarized parallel to the z axis. Let {αn}n=1∞ be a distinct set of angles in [ - π, π] and μ a complex number. Then, necessary and sufficient conditions are given for the set {(1 - μ)FD(θ;αn) + μFN(θ;αn)}n = 1∞ to be complete in L2[ - π, π]. Applications, together with numerical examples, are given to the inverse scattering problem of determining the shape of the cylinder from a knowledge of the far-field data.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670120605
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  • 6
    Electronic Resource
    Electronic Resource
    Some solutions for the spin glass system and for systems originating from it (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 31-41 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the spin glass system the solutions, u = νΦ and u = νx/|x| are considered, where ν is a scalar function and Φε∝3 is constant. For a system originating from the spin glass one, a solution u = tan[q(|x|/t)]x/|x| is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130104
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  • 7
    Electronic Resource
    Electronic Resource
    Masthead (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990) 
    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.1670130201
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  • 8
    Electronic Resource
    Electronic Resource
    A study of a non-linear kinetic model for an ionized gas (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 95-109 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A non-linear one-dimensional kinetic model for an ionized gas is considered. In this model the collisions between charged and neutral particies and the field generated by the charges are taken into account. The Cauchy problem for the resulting system of equations is examined. An existence and uniqueness theorem of a global in time solution is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130202
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  • 9
    Electronic Resource
    Electronic Resource
    A two-species plasma in the limit of large ion mass (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 159-167 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Classical solutions of the relativistic Vlasov-Maxwell system are considered, describing a collisionless plasma with two species of particles. ions and electrons. It is shown that as the ion mass m tends to infinity, the corresponding solution of the relativistic Vlasov-Maxwell system tends to the solution of a system, in which the ions are given by a fixed ion background and only the electrons move. The convergence is uniform on compact time intervals, with an asymptotic convergence rate of m-1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130206
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  • 10
    Electronic Resource
    Electronic Resource
    Asymptotic analysis of the quantum Liouville equation (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 143-157 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present an asymptotic analysis of the quantum Liouville equation with respect to the Planck's constant, which models the temporal evolution of the (quasi)distribution of an ensemble of electrons under the action of a potential. We consider two cases: firstly a smooth potential, and secondly a potential modelled by a δ-distribution. In both cases the zeroth-order term behaves classically. In the smooth case the classical Liouville equation is satisfied and in the case for the δ-potential an interface condition is derived, so that everything is reflected at the potential barrier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130205
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