Some results based on maximal regularity regarding population models with age and spatial structure

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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.

Keywords

Population models Age and spatial structure Maximal regularity Bifurcation theory 

Mathematics Subject Classification

35K59 35B32 47D06 92D25 47H07 

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© Orthogonal Publishing and Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Angewandte MathematikLeibniz Universität HannoverHannoverGermany

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