## Elements of approximation theory by Leopoldo Nachbin By Leopoldo Nachbin

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Nonlinear diffUsion problems in age- structured population dynamias. M. (1980). Model stability and instability in age structured populations. J. Theor. BioI. 86: 709-730. M. & Saleem, M. (1982). A predator-prey model with age structure. J. Math. BioI. 14: 231-250. Diekmann, O. (1980). Volterra integral equations and semigroups of operators. MC Report TW 197. M. & Thieme, H. (in preparation). On the stability of the cell size distribution. , Aldenberg, T. J. (preprint 1983). Growth, fission and the stable size distribution.

Renewal theorems for linear periodic Volterra integral equations, to appear. : pear. ~ and w = w(t,x) their mean flux. dxu , t-o(u) ~ 0 and (1) would be the usual diffusion equation. In contrast, modelling aggregation would require the opposite sign of ~o leading to an ill-posed problem for (1) in general. ';)xu + l#A~3u OX compare [3}, for example, where aggregation in a morphogenetic context is described. It can be shown, that under suitable hypotheses on the "attractivity" coefficient )(o(u) the equation (1),(3) has locally stable aggregation patterns (joint work with Hans Engler, in preparation).

Differential Equations 39 (1981), 345 - 377. 2. Aulbach, Invariant Manifolds with Asymptotic Phase. Nonlinear Analysis TMA 6 (1982), 817 - 827. 3. Aulbach, Approach to Hyperbolic Manifolds of Stationary Solutions. in "Equadiff 82", Lecture Notes in Mathematics, Springer, to appear. 4. Aulbach, Continuous and Discrete Dynamics near Manifolds of Equilibria. Preprint University of WUrzburg. 5. Hadeler, Convergence to Equilibrium in the Classical Model of Population Genetics. , to appear. 6. Kimura, An Introduction to Population Genetics Theory.