REISSIG Michael, SMITH James,
$L^p-L^q$ estimate for wave equation with bounded time dependent coefficient.
Hokkaido Mathematical Journal, 34 (2005) pp.541-586
The goal of the present paper is to derive $L^p-L^q$ estimates for wave equations with a bounded time dependent coefficient. A classification of the oscillating behaviour of the coefficient is given. This classification determines in an essential way the possibility of deriving $L^p-L^q$ decay estimates.
|Uncontrolled Keywords||wave equation, oscillating time dependent coefficient, WKB-representation,Fourier multipliers, Floquet's theory|