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  • Numerical Methods and Modeling  (3)
  • Wiley-Blackwell  (3)
  • American Meteorological Society (AMS)
  • Cell Press
  • 1
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 761-772 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For a linear coagulation kernel and a constant fragmentation kernel we prove the existence of equilibrium solutions and examine asymptotic properties for time-dependent solutions which are proved to converge to the equilibria. The rate of the convergence is estimated. It is shown also that all time-dependent solutions with the same density can tend to only one particular steady-state solution. In this sense the equilibrium solution is proved to be unique. Existence, uniqueness and mass conservation of time-dependent solutions has been proved in a previous paper by the authors [10].
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 171-185 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that the non-linear coagulation-fragmentation equation with constant kernels has a unique equilibrium solution. This equilibrium solution is given explicitly in terms of the initial data and the kernels. Weak L1 convergence of time-dependent solutions to the unique equilibrium is demonstrated via an invariance principle employing a suitable lower semicontinuous Lyapunov functional.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 571-591 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove global existence and uniqueness to the initial value problem for the coagulation-fragmentation equation for an unbounded coagulation kernel with possible linear growth at infinity and a fragmentation kernel from a very large class of unbounded functions. We show that the solutions satisfy the mass conservation law.
    Type of Medium: Electronic Resource
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