Abstract
We consider a size structured population model in the state space L 2(0,1) and compute the extension of the solution semigroup to the extrapolation space V* = (dom A*)*, A being the infinitesimal generator of the solution semigroup. Furthermore we prove equivalence of the problem on the extrapolation space to a variational formulation.
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Banks, H.T., Kappel, F., Wang, C. (1991). Weak solutions and differentiability for size structured population models. In: Desch, W., Kappel, F., Kunisch, K. (eds) Estimation and Control of Distributed Parameter Systems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 100. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6418-3_2
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DOI: https://doi.org/10.1007/978-3-0348-6418-3_2
Publisher Name: Birkhäuser, Basel
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