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2 results

  • A CELL GROWTH MODEL ADAPTED FOR THE MINIMUM CELL SIZE DIVISION

  • Part of
  • B. VAN BRUNT, S. GUL, G. C. WAKE
  • Journal:
    The ANZIAM Journal / Volume 57 / Issue 2 / October 2015
    Published online by Cambridge University Press:
    01 December 2015, pp. 138-149
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  • We study a cell growth model with a division function that models cells which divide only after they have reached a certain minimum size. In contrast to the cases studied in the literature, the determination of the steady size distribution entails an eigenvalue that is not known explicitly, but is defined through a continuity condition. We show that there is a steady size distribution solution to this problem.

  • Quasi-linear parabolic partial differential equations with delays in the highest order spatial derivatives

  • Part of
  • Jiongmin Yong, Liping Pan
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 54 / Issue 2 / April 1993
    Published online by Cambridge University Press:
    09 April 2009, pp. 174-203
    Print publication:
    April 1993
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  • A class of functional differential equations in some Hilbert space are studied. The results are applicable to many quasi-linear parabolic paratial differential equations with (possibly) countably many discrete delays and finitely many distributed delays in the highest order spatial derivatives. For the linear case, an evolution operator on the underline space H is introduced, via which a variation of constant formula for the solution of the equation in the underline space H is derived. Some spectral properties of the generator of the solution semigroup defined on some appropriate space are discussed as well.