Relative bounded perturbation of abstract cauchy problem

Yu Hsien Chang, Cheng Hong Hong

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we study the perturbed abstract Cauchy equation du(t) dt = (A + B)u(t) with initial condition u(0) = x, where A is a generator of a C-semigroup on a Banach space X and B is a relatively bounded linear operator on X. We show that if the perturbation operator B is an A-bounded linear operator which commutates with C and its Abound is sufficiently small, then (A + B) generates a C-semigroup {V(t)}t≥0 on X, and hence the perturbed abstract Cauchy problem has a unique mild solution as long as the initial data x is in the subspace [Im(C)]. It is remarkable that we can directly apply these results to some differential equations.

Original languageEnglish
Pages (from-to)555-575
Number of pages21
JournalFar East Journal of Mathematical Sciences
Volume29
Issue number3
Publication statusPublished - 2008 Jun 1

Keywords

  • C-semigroup
  • Perturbation
  • Relatively bounded

ASJC Scopus subject areas

  • Mathematics(all)

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