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  • 1
    Electronic Resource
    Electronic Resource
    Mixing and some integro-functional equations (1990)
    Springer
    Aequationes mathematicae 40 (1990), S. 78-82 
    Details
    ISSN: 1420-8903
    Keywords: Primary 45A05 ; Secondary 45A35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is proved that the operatorP: L 1 (0, ∞) →L 1(0, ∞), given byPg(z) = ∫ z/c ∞ [g(x)/cx]dx, is completely mixing, i.e.,∥P n g∥ 1 → 0 forg ∈L 1(0, ∞) with ∫g dx = 0. This implies that, forc ∈ (0, 1), each continuous and bounded solution of the equationf(x)=∫ 0 cx f(t)dt/(cx) (x ∈ (0, 1]) is constant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02112282
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Stability properties of proliferatively coupled cell replication models (1991)
    Springer
    Acta biotheoretica 39 (1991), S. 1-14 
    Details
    ISSN: 1572-8358
    Keywords: Hematological diseases ; first order partial differential equations ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract To address the possibility that proliferative disorders may originate from interactions between multiple populations of proliferating and maturing cells, we formulate a model for this process as a set of coupled nonlinear first order partial differential equations. Using recent results for the asymptotic behaviour of the solutions to this model, we demonstrate that there exists a region of coupling coefficients, maturation rates, and proliferation rates that will guarantee the stable coexistence of coupled cellular populations. The analysis shows that increases in the coupling between populations may ultimately lead to a loss of stability. Furthermore, the analysis indicates that increases (decreases) in the maturation and/or proliferation rates above (below) critical levels will lead either to instability in the populations or the destruction of one population and the persistence of the other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046404
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    Paper (German National Licenses)
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