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| $L_p?L_q$ DECAY ESTIMATES FOR HYPERBOLIC EQUATIONS WITH OSCILLATIONS IN COEFFICIENTS |
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Citation： |
M. REISSIG,K. YAGDJIAN.$L_p?L_q$ DECAY ESTIMATES FOR HYPERBOLIC EQUATIONS WITH OSCILLATIONS IN COEFFICIENTS[J].Chinese Annals of Mathematics B,2000,21(2):153~164 |
| Page view： 1254
Net amount： 843 |
Authors： |
M. REISSIG; K. YAGDJIAN |
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| Abstract： |
This work is concerned with the proof of $L_p-L_q$ decay estimates
for solutions of the Cauchy problem for $u_{tt} - \la^2(t)b^2(t)
\bigi u = 0$. The coefficient consists of an increasing smooth
function $\la$ and an oscillating smooth and bounded function $b$
which are uniformly separated from zero. The authors' main interest is
devoted to the critical case where one has an interesting
interplay between the growing and the oscillating part. |
Keywords： |
$L_p?L_q$ decay estimates, Wave equation, Fourier multipliers |
Classification： |
35L70, 35L80, 35B20 |
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