Klein-Gordon type decay rates for wave equations with time-dependent coefficients

Reissig, Michael; Yagdjian, Karen

Banach Center Publications, Tome 51 (2000), p. 189-212 / Harvested from The Polish Digital Mathematics Library

Résumé

This work is concerned with the proof of $L_{p} - L_{q}$ decay estimates for solutions of the Cauchy problem for the Klein-Gordon type equation $u_{t t} - λ^{2} (t) b^{2} (t) (Δ u - m^{2} u) = 0$ . The coefficient consists of an increasing smooth function $λ$ and an oscillating smooth and bounded function b which are uniformly separated from zero. Moreover, $m^{2}$ is a positive constant. We study under which assumptions for λ and b one can expect as an essential part of the decay rate the classical Klein-Gordon decay rate n/2(1/p-1/q).

Publié le : 2000-01-01

Zbl 0983.35078

EUDML-ID : urn:eudml:doc:209057

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     author = {Reissig, Michael and Yagdjian, Karen},
     title = {Klein-Gordon type decay rates for wave equations with time-dependent coefficients},
     journal = {Banach Center Publications},
     volume = {51},
     year = {2000},
     pages = {189-212},
     zbl = {0983.35078},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv52z1p189bwm}
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Reissig, Michael; Yagdjian, Karen. Klein-Gordon type decay rates for wave equations with time-dependent coefficients. Banach Center Publications, Tome 51 (2000) pp. 189-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv52z1p189bwm/

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