Characterization of polynomial decay rate for the solution of linear evolution equation
Liu, Zhyangyi ; Rao, Bopeng
HAL, hal-00129703 / Harvested from HAL
Text on HAL
In this paper, we study the decay rate of solutions to strongly stable, but not exponentially stable linear evolution equations. It is known that the resolvent operator of such an equation must be undounded on the imaginary axis. Our main result is an estimate of the decay rate when the unboundedness is of polynomial order. We then apply our main theorem to three strongly stable but not explnentially stable systems to obtain the decay rate, which is not available in the literature.
Publié le : 2004-07-05
Classification:  "polynomial decay rate,  semigroup,  domain frequency",  polynomial decay rate,  domain frequency,  35B40, 35L20,  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 
@article{hal-00129703,
     author = {Liu, Zhyangyi and Rao, Bopeng},
     title = {Characterization of polynomial decay rate for the solution of linear evolution equation},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00129703}
}

Liu, Zhyangyi; Rao, Bopeng. Characterization of polynomial decay rate for the solution of linear evolution equation. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129703/