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2007 On integrated semigroups and age structured models in {$L^p$} spaces
Pierre Magal, Shigui Ruan
Differential Integral Equations 20(2): 197-239 (2007). DOI: 10.57262/die/1356039513


In this paper, we first develop some techniques and results for integrated semigroups when the generator is not a Hille-Yosida operator and is non-densely defined. Then we establish a theorem of Da Prato and Sinestrari's type for the nonhomogeneous Cauchy problem and prove a perturbation theorem. In particular, we obtain necessary and sufficient conditions for the existence of mild solutions for non-densely defined non-homogeneous Cauchy problems. Next we extend the results to $L^{p}$ spaces and consider the semilinear and non-autonomous problems. Finally we apply the results to studying age-structured models with dynamic boundary conditions in $L^{p}$ spaces. We also demonstrate that neutral delay differential equations in $L^{p}$ can be treated as special cases of the age-structured models in an $L^{p}$ space.


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Pierre Magal. Shigui Ruan. "On integrated semigroups and age structured models in {$L^p$} spaces." Differential Integral Equations 20 (2) 197 - 239, 2007.


Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35238
MathSciNet: MR2294465
Digital Object Identifier: 10.57262/die/1356039513

Primary: 47D62
Secondary: 34G10 , 35K57 , 47D06 , 92D25 , 92D30

Rights: Copyright © 2007 Khayyam Publishing, Inc.


Vol.20 • No. 2 • 2007
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