Stability of Fredholm type integro-parabolic equations
The author derives stability conditions for a class of linear time-variant integro-parabolic equations of Fredholm type. The main tool of the paper is a combined usage of the so called particular inner product with spectral properties of integral operators. The proposed approach allows one to reduce the stability problem for integro-parabolic equations to the stability analysis of ordinary integrodifferential equations of Fredholm type or ordinary differential equations. In particular the results obtained in the paper generalize the Wazewski estimate from the theory of ordinary differential equations. A few words about the contents. It consists of 6 sections. The first section is devoted to some definitions. The basic lemma giving solution estimates is formulated in Section 2. In Section 3 the author introduces the notion of the particular inner product and proves the basic lemma. The main object of the paper: abstract integrodifferential equations are investigated in Section 4. Bounds for the spectrum of integral operators are presented in Section 5. Section 6 is devoted to the stability analysis of coupled systems of integrodifferential equations.
scientific article; zbMATH DE number 1449210
scientific article