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7997 results in Fluid dynamics and solid mechanics

Page 34 of 400

  • ANZ VOLUME 64 ISSUE 1 COVER AND BACK MATTER

  • Journal:
    The ANZIAM Journal / Volume 64 / Issue 1 / January 2022
    Published online by Cambridge University Press:
    27 May 2022, pp. b1-b6
    • Article
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Attractors for Semigroups and Evolution Equations
  • Olga A. Ladyzhenskaya
  • Foreword by Gregory A. Seregin, Varga K. Kalantarov, Sergey V. Zelik
  • Published online:
    19 May 2022
    Print publication:
    09 June 2022
  • In this volume, Olga A. Ladyzhenskaya expands on her highly successful 1991 Accademia Nazionale dei Lincei lectures. The lectures were devoted to questions of the behaviour of trajectories for semigroups of nonlinear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many initial boundary value problems for dissipative partial differential equations. This work, for which Ladyzhenskaya was awarded the Russian Academy of Sciences' Kovalevskaya Prize, reflects the high calibre of her lectures; it is essential reading for anyone interested in her approach to partial differential equations and dynamical systems. This edition, reissued for her centenary, includes a new technical introduction, written by Gregory A. Seregin, Varga K. Kalantarov and Sergey V. Zelik, surveying Ladyzhenskaya's works in the field and subsequent developments influenced by her results.

  • DISPERSAL OF HYDROGEN IN THE RETINA—A THREE-LAYER MODEL

  • Part of
  • W. F. MANSOOR, G. C. HOCKING, D. E. FARROW
  • Journal:
    The ANZIAM Journal / Volume 64 / Issue 1 / January 2022
    Published online by Cambridge University Press:
    10 May 2022, pp. 1-22

  • Two simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model.

Page 34 of 400