Opuscula Math. 31, no. 2 (2011), 279-288
http://dx.doi.org/10.7494/OpMath.2011.31.2.279
Opuscula Mathematica
Polynomial stability of evolution operators in Banach spaces
Megan Mihail
Traian Ceauşu
Magda Luminiţa Ramneanţu
Abstract. The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.
Keywords: evolution operator, polynomial stability, exponential stability.
Mathematics Subject Classification: 34D05, 34E05.
- Megan Mihail
- Academy of Romanian Scientists, Independenţei 54, Bucharest, 050094, Romania
- Departament of Mathematics, West University of Timişoara, Bd. V. Parvan, Nr.4, 300223, Timişoara, Romania
- Traian Ceauşu
- Departament of Mathematics, West University of Timişoara, Bd. V. Parvan, Nr.4, 300223, Timişoara, Romania
- Magda Luminiţa Ramneanţu
- Departament of Mathematics, West University of Timişoara, Bd. V. Parvan, Nr.4, 300223, Timişoara, Romania
- Received: 2010-06-29.
- Revised: 2010-07-23.
- Accepted: 2010-10-07.
