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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The stability of positive semigroups on $ L\sb p$ spaces


Author: Lutz Weis
Journal: Proc. Amer. Math. Soc. 123 (1995), 3089-3094
MSC: Primary 47D06; Secondary 34G10, 35P05, 47D07, 47N20
MathSciNet review: 1273529
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Abstract: For a positive semigroup $ {T_t}$ on $ {L_p}(\Omega ,m)$ with generator A, the growth bound of $ ({T_t})$ equals the spectral bound of A. In particular, if $ s(A) < 0$, the mild solutions of the Cauchy problem $ u' = Au$ are asymptotically stable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1273529-2
PII: S 0002-9939(1995)1273529-2
Article copyright: © Copyright 1995 American Mathematical Society