In a recent paper we presented a general perturbation result for generators of \(C_0\)-semigroups, c.f. Theorem 2.1 below. The aim of the present work is to replace, in case the unperturbed semigroup is analytic, the various admissibility conditions appearing in this result by simpler inclusion assumptions on the domain and the range of the perturbation. This is done in Theorem 2.4 and allows to apply our results also in situations which are only in part governed by analytic semigroups. The power of our approach to treat in a unified and systematic way wide classes of PDE’s is illustrated by a generic example, a degenerate differential operator with generalized Wentzell boundary conditions, a reaction diffusion equation with unbounded delay and a perturbed Laplacian.

Perturbation of analytic semigroups and applications to partial differential equations

ENGEL, KLAUS JOCHEN OTTO
2017

Abstract

In a recent paper we presented a general perturbation result for generators of \(C_0\)-semigroups, c.f. Theorem 2.1 below. The aim of the present work is to replace, in case the unperturbed semigroup is analytic, the various admissibility conditions appearing in this result by simpler inclusion assumptions on the domain and the range of the perturbation. This is done in Theorem 2.4 and allows to apply our results also in situations which are only in part governed by analytic semigroups. The power of our approach to treat in a unified and systematic way wide classes of PDE’s is illustrated by a generic example, a degenerate differential operator with generalized Wentzell boundary conditions, a reaction diffusion equation with unbounded delay and a perturbed Laplacian.
File in questo prodotto:
File Dimensione Formato  
Engel-Adler-Bombieri-JEE_2017.pdf

non disponibili

Descrizione: Articolo principale versione finale
Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 597.11 kB
Formato Adobe PDF
597.11 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/110450
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact