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

• Autorzy: Michael Reissig , Karen Yagdjian
• Języki publikacji: EN

Abstrakty

EN

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).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 52
• Numer: 1
• Strony: 189-212

Daty

wydano

2000

Twórcy

autor

Michael Reissig

• Faculty of Mathematics and Computer Science, Technical University Bergakademie Freiberg, Bernhard von Cotta Str. 2, 09596 Freiberg, Germany

autor

Karen Yagdjian

• Institute of Mathematics, University of Tsukuba , Tsukuba, Ibaraki 305, Japan

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