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

Michael Reissig; Karen Yagdjian

Banach Center Publications (2000)

- Volume: 52, Issue: 1, page 189-212
- ISSN: 0137-6934

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topReissig, Michael, and Yagdjian, Karen. "Klein-Gordon type decay rates for wave equations with time-dependent coefficients." Banach Center Publications 52.1 (2000): 189-212. <http://eudml.org/doc/209057>.

@article{Reissig2000,

abstract = {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 $u_\{tt\} - λ^2(t)b^2(t) (Δu - m^\{2\}u) = 0$. 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).},

author = {Reissig, Michael, Yagdjian, Karen},

journal = {Banach Center Publications},

keywords = {- decay estimates},

language = {eng},

number = {1},

pages = {189-212},

title = {Klein-Gordon type decay rates for wave equations with time-dependent coefficients},

url = {http://eudml.org/doc/209057},

volume = {52},

year = {2000},

}

TY - JOUR

AU - Reissig, Michael

AU - Yagdjian, Karen

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

JO - Banach Center Publications

PY - 2000

VL - 52

IS - 1

SP - 189

EP - 212

AB - 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 $u_{tt} - λ^2(t)b^2(t) (Δu - m^{2}u) = 0$. 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).

LA - eng

KW - - decay estimates

UR - http://eudml.org/doc/209057

ER -

## References

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