On characterization and perturbation of local $C$-semigroups
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- by Yuan-Chuan Li and Sen-Yen Shaw PDF
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Abstract:
Let $S(\cdot )$ be a $(C_0)$-group with generator $-B$, and let $\{T(t);0\le t<\tau \}$ be a local $C$-semigroup commuting with $S(\cdot )$. Then the operators $V(t):=S(-t)T(t)$, $0\le t<\tau$, form a local $C$-semigroup. It is proved that if $C$ is injective and $A$ is the generator of $T(\cdot )$, then $A+B$ is closable and $\overline {A+B}$ is the generator of $V(\cdot )$. Also proved are a characterization theorem for local $C$-semigroups with $C$ not necessarily injective and a theorem about solvability of the abstract inhomogeneous Cauchy problem: $uβ(t)=Au(t)+Cf(t), 0<t<\tau ;\ u(0)=Cx.$References
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Additional Information
- Yuan-Chuan Li
- Affiliation: Department of Applied Mathematics, National Chung-Hsing University, Taichung, 402 Taiwan
- Email: ycli@amath.nchu.edu.tw
- Sen-Yen Shaw
- Affiliation: Graduate School of Engineering, Lunghwa University of Science and Technology, Gueishan, Taoyuan, 333 Taiwan
- Email: shaw@math.ncu.edu.tw
- Received by editor(s): August 8, 2005
- Received by editor(s) in revised form: November 7, 2005
- Published electronically: September 26, 2006
- Additional Notes: This research was supported in part by the National Science Council of Taiwan.
- Communicated by: Joseph A. Ball
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1097-1106
- MSC (2000): Primary 47D06, 47D60
- DOI: https://doi.org/10.1090/S0002-9939-06-08549-2
- MathSciNet review: 2262911