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arXiv · 1709.04445

Some Results Based on Maximal Regularity Regarding Population Models with Age and Spatial Structure

Christoph Walker
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Abstract

We review some results on abstract linear and nonlinear population models with age and spatial structure. The results are mainly based on the assumption of maximal $L_p$-regularity of the spatial dispersion term. In particular, this property allows us to characterize completely the generator of the underlying linear semigroup and to give a simple proof of asynchronous exponential growth of the semigroup. Moreover, maximal regularity is also a powerful tool in order to establish the existence of nontrivial positive equilibrium solutions to nonlinear equations by fixed point arguments or bifurcation techniques. We illustrate the results with examples.

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Christoph Walker. 2017-09-13. Some Results Based on Maximal Regularity Regarding Population Models with Age and Spatial Structure. https://arxiv.org/abs/1709.04445

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