Semilinear perturbations of Hille-Yosida operators

• Autorzy: Horst R. Thieme , Hauke Vosseler
• Języki publikacji: EN

Abstrakty

EN

The semilinear Cauchy problem
(1) u'(t) = Au(t) + G(u(t)), $u(0) = x ∈ \overline{D(A)}$,
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,
$B(λ - A)^{-1}x = λ ∫_0^∞ e^{-λt} V(s)xds$,
where V is of suitable small strong variation on some interval [0,ε). We will prove the existence of a semiflow on $[0,∞) × \overline{D(A)}$ 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.

Kategorie tematyczne

• 47J35: Nonlinear evolution equations
• 92D25: Population dynamics (general)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2003
• Tom: 63
• Numer: 1
• Strony: 87-122

Daty

wydano

2003

Twórcy

autor

Horst R. Thieme

• Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, U.S.A.

autor

Hauke Vosseler

• Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, U.S.A.

Identyfikatory

DOI

10.4064/bc63-0-3