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  • 1
    Electronic Resource
    Electronic Resource
    Singularly Perturbed Linear and Semilinear Hyperbolic Systems: Kinetic Theory Approach to Some Folk’s Theorems (1997)
    Springer
    Acta applicandae mathematicae 49 (1997), S. 199-228 
    Details
    ISSN: 1572-9036
    Keywords: singular perturbations ; asymptotic expansion ; hyperbolic systems ; damped wave equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The fact that a solution of a wave equation with strong damping can be approximated by a solution of an appropriate diffusion equation has been common knowledge to physicists and mathematicians for a few decades. In numerous branches of science one can find attempts to prove this results by various ad hoc methods. However, it seems to be difficult to trace a rigorous and exhaustive treatment of the subject. By using a recently developed asymptotic procedure, first applied in kinetic theory, we present a systematic approach to a wide spectrum of singularly perturbed hyperbolic problems and we also hope that our method will provide new insight into the field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005882912151
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Generation results forB-bounded semigroups (1998)
    Springer
    Annali di matematica pura ed applicata 175 (1998), S. 307-326 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In [3]A. Bellini-Morante defined and analysed a new one-parameter family of bounded operators which he called a B-bounded semigroup. The definition was motivated by an example from the transport theory where the evolution generated by an operator A was in a certain sense controlled by another operator B. In this paper we show that a given pair (A, B) generates a B-bounded semigroup if and only if in a certain extrapolation space related to the operator B, the closure of A generates a semigroup and we also address some related topics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01783690
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Diffusion limit for the linear boltzmann equation of the neutron transport theory (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1071-1087 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we present the asymptotic analysis of the linear Boltzmann equation for neutrons with a small positive parameter ∊ related to the mean free path, based upon the Chapman-Enskog procedure of the kinetic theory. We prove that if proper initial conditions derived by considering initial layer solutions are used, the diffusion equation gives the uniform approximation to the neutron density function with the O(∊2) accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171306
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Asymptotic Analysis of Abstract Linear Kinetic Equations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 481-505 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we provide a theory of the asymptotic expansion for an abstract kinetic equation. We show that the modified Chapman-Enskog procedure, introduced in [19], gives the error of order of ε2, uniformly in time, on the second level of approximation and in particular that the zeroth moment of the solution (the spatial density of particles) can be approximated by the solution of the diffusion-type equation with the same accuracy. The theory is applied to several types of kinetic equations with the Fokker-Planck collision operator.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    Remark on a trace theorem for transmission problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 413-421 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we discuss elliptic transmission problems of second order in plane non-smooth domains with non-homogeneous boundary data. It is known that if the boundary data are homogeneous, then the variational solution of the transmission problem admits a representation as a sum of a regular function and certain singular functions, analogous to that encountered in boundary value problems on corner domains. We determine for which domains arbitrary non-homogeneous boundary data can be reduced to the homogeneous ones preserving availability of the representation formula. In the remaining cases we find the compatibility conditions for the data which also yield such a reduction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180506
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    Paper (German National Licenses)
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