## The stability of positive semigroups on $L_ p$ spaces

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- by Lutz Weis PDF
- Proc. Amer. Math. Soc.
**123**(1995), 3089-3094 Request permission

## 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

- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**123**(1995), 3089-3094 - MSC: Primary 47D06; Secondary 34G10, 35P05, 47D07, 47N20
- DOI: https://doi.org/10.1090/S0002-9939-1995-1273529-2
- MathSciNet review: 1273529