July  1999, 5(3): 651-662. doi: 10.3934/dcds.1999.5.651

Pazy-type characterization for differentiability of propagators of higher order Cauchy problems in Banach spaces

1. 

Department of Mathematics, University of Science and Technology of China, Hefei 230026, China, China

Received  March 1998 Revised  May 1999 Published  May 1999

Of concern is the differentiability of the propagators of higher order Cauchy problem

$u^{(n)}(t) +\sum_{k=0}^{n-1}A_ku^{(k)}(t)=0, t\geq 0,$

$u^{(k)}(0) = u_k, 0\leq k\leq n-1,

where $A_0, A_1,\ldots, A_{n-1}$ are densely defined closed linear operators on a Banach space. A Pazy-type characterization of the infinitely differentiable propagators of the Cauchy problem is obtained. Moreover, two related sufficient conditions are given.

Citation: Ti-Jun Xiao, Jin Liang. Pazy-type characterization for differentiability of propagators of higher order Cauchy problems in Banach spaces. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 651-662. doi: 10.3934/dcds.1999.5.651
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