On integrated semigroups and age structured models in {$L^p$} spaces
By Pierre Magal, Shigui Ruan. Differential and Integral Equations, 2007
101 citations recorded by the source corpus.
In this paper, we first develop some techniques and results for integrated semigroups when the generator is not a Hille-Yosida opera- tor 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 suffi- cient conditions for the existence of mild solutions for non-densely de- fined non-homogeneous Cauchy problems. Next we extend the results to L p spaces and consider the semilinear and non-autonomous prob- lems. 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/d4aa48ce785ddab3b2101171b5bcbf762c6288e0
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Citations in the corpus
- Travelling wave solutions for an infection-age structured model with diffusion (2009, methodology): “2) as an abstract evolution equation we use the approach of Thieme [15] (see also [16, 17, 13] and references therein for more detailed description of the problem).”
- Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems (2008, methodology): “1 in [10], and the fact that if ρ(A) = ∅ then ρ(A)= ρ(A0), one obtains the following lemma.”
- On semilinear Cauchy problems with non-dense domain (2009, methodology): “The uniqueness of the solution with initial value x in BX0(0;") follows from the fact that F is locally Lipschitz continuous around 0 and by using the arguments of Lemma 3.3 in Magal and Ruan [ 22 ].”
- Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity (2009, background): “\? is locally Lipschitz continuous if p = 1 [37] and of bounded semi^p-variation if 1 < p < oo [28, 41].”
- Hopf bifurcation for non-densely defined Cauchy problems (2011, methodology): “[32], Magal and Ruan [34], and Chu et al.”