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Cauchy problems with state-dependent time evolution

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Abstract

We consider a class of quasilinear Cauchy problems which frequently arise in the context of structured population dynamics and which have in common that they can be reduced to a semilinear problem by a time-scale argument. We prove existence and uniqueness of solutions, study positivity and regularity properties, and prove the principle of linearized stability. These abstract results are applied to a model describing the dynamics of a size-structured cell population whose individuals are subject to a nonlinear growth law.

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Authors and Affiliations

  1. Department of Mathematics, University of Tübingen, Auf der Morgenstelle 10, 7400, Tübingen, Federal Republic of Germany

    A. Grabosch

  2. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands

    H. J. A. M. Heijmans

Authors
  1. A. Grabosch
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  2. H. J. A. M. Heijmans
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Additional information

This work was done during a visit to the Centre of Mathematics and Computer Science, Amsterdam, in the academic year 1987/1988. The stay was supported by the Stichting Mathematisch Centrum. I cordially thank my hosts for making this stay possible and very much enjoyable. Especially, I thank all the members of the “Applied Mathematics Department” for their great hospitality and for many valuable discussions.

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Grabosch, A., Heijmans, H.J.A.M. Cauchy problems with state-dependent time evolution. Japan J. Appl. Math. 7, 433–457 (1990). https://doi.org/10.1007/BF03167853

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  • DOI: https://doi.org/10.1007/BF03167853

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