Non uniform decay of the total energy of the dissipative wave equation
Nishiyama, Hisashi
Osaka J. Math., Tome 46 (2009) no. 1, p. 461-477 / Harvested from Project Euclid
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Kawashita, Nakazawa, and Soga [3] give a necessary condition for the uniform energy decay of the dissipative wave equation whose principal term has constant coefficients. In their proof, they construct asymptotic solutions for a suitable family of the Cauchy data. In this paper, instead of the asymptotic solutions, we consider the semiclassical measure associated with the family and extend this result to the variable coefficient case. Moreover we give some lower bound estimate for the energy decay.
Publié le : 2009-06-15
Classification:  35L05,  35L15 
@article{1245415679,
     author = {Nishiyama, Hisashi},
     title = {Non uniform decay of the total energy of the dissipative wave equation},
     journal = {Osaka J. Math.},
     volume = {46},
     number = {1},
     year = {2009},
     pages = { 461-477},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245415679}
}

Nishiyama, Hisashi. Non uniform decay of the total energy of the dissipative wave equation. Osaka J. Math., Tome 46 (2009) no. 1, pp.  461-477. http://gdmltest.u-ga.fr/item/1245415679/