JournalsrlmVol. 29, No. 4pp. 589–596

Stability of evolution equations with small commutators in a Banach space

  • Michael Gil'

    Ben Gurion University of the Negev, Beer-Sheva, Israel
Stability of evolution equations with small commutators in a Banach space cover
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Abstract

Let AA be a generator of a C0C_0-semigroup in a Banach space X\mathcal X, and B(t)B(t) (t0)(t\ge 0) be a variable bounded piece-wise strongly continuous operator in X\mathcal X. We consider the equation dy(t)/dt=(A+B(t))y(t)dy(t)/dt = (A+B(t))y(t) (t0)(t\ge 0). It is assumed that the commutator K(t)=AB(t)B(t)AK(t)=AB(t)-B(t)A is a bounded operator. Under that condition, exponential stability conditions are derived in terms of the commutator.

Cite this article

Michael Gil', Stability of evolution equations with small commutators in a Banach space. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 4, pp. 589–596

DOI 10.4171/RLM/822