Hokkaido Mathematical Journal

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

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Abstract

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.

MSC(Primary)35L15
MSC(Secondary)35L05
Uncontrolled Keywordswave equation, oscillating time dependent coefficient, WKB-representation,Fourier multipliers, Floquet's theory