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Exponential Stability


Exponential stability of a strongly continuous semigroup (T(t))_(t>=0) on a Banach space is the existence of constants M>=1 and omega>0 such that

 ||T(t)||<=Me^(-omegat)

for every t>=0. Thus the operator norm of T(t) decays at least exponentially as t->infty. Exponential stability implies strong stability, but strong stability need not imply exponential stability.


See also

Gearhart-Prüss-Huang Theorem, Semigroup Stability, Strong Stability, Strongly Continuous Semigroup

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References

Engel, K.-J. and Nagel, R. One-Parameter Semigroups for Linear Evolution Equations. New York: Springer-Verlag, 2000.

Cite this as:

Weisstein, Eric W. "Exponential Stability." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ExponentialStability.html

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