TY - JOUR
A2 - Krutitskii, Pavel A.
AU - Gil', Michael
PY - 2013
DA - 2013/04/28
TI - Integrally Small Perturbations of Semigroups and Stability of Partial Differential Equations
SP - 207581
VL - 2013
AB - Let A be a generator of an exponentially stableoperator semigroup in a Banach space,and let Ct t≥0 be a linear bounded variable operator. Assuming that ∫0tCsds is sufficiently small in a certain sense for the equationdx/dt=Ax+C(t)x, we derive exponential stability conditions. Besides, we do not require that for each t0≥0, the “frozen” autonomous equation dx/dt=Ax+C(t0)x is stable. In particular, we considerevolution equations with periodic operator coefficients. These results are applied to partial differential equations.
SN - 2356-7082
UR - https://doi.org/10.1155/2013/207581
DO - 10.1155/2013/207581
JF - International Journal of Partial Differential Equations
PB - Hindawi Publishing Corporation
KW -
ER -