The semilinear Cauchy problem (1) u’(t) = Au(t) + G(u(t)), , with a Hille-Yosida operator A and a nonlinear operator G: D(A) → X is considered under the assumption that ||G(x) - G(y)|| ≤ ||B(x -y )|| ∀x,y ∈ D(A) with some linear B: D(A) → X, , where V is of suitable small strong variation on some interval [0,ε). We will prove the existence of a semiflow on that provides Friedrichs solutions in L₁ for (1). If X is a Banach lattice, we replace the condition above by |G(x) - G(y)| ≤ Bv whenever x,y,v ∈ D(A), |x-y| ≤ v, with B being positive. We illustrate our results by applications to age-structured population models.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc63-0-3,
author = {Horst R. Thieme and Hauke Vosseler},
title = {Semilinear perturbations of Hille-Yosida operators},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {87-122},
zbl = {1073.47063},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc63-0-3}
}
Horst R. Thieme; Hauke Vosseler. Semilinear perturbations of Hille-Yosida operators. Banach Center Publications, Tome 60 (2003) pp. 87-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc63-0-3/