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Representation theorem for the solution of weakly hyperbolic equations with fast oscillating coefficients

100%

Kinoshita T., Yagdjian K.

Banach Center Publications

2003

tom 60

nr 1

121-130

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

100%

Reissig M., Yagdjian K.

Banach Center Publications

2000

tom 52

nr 1

189-212

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).

Ograniczanie wyników

2 Banach Center Publications

2 Yagdjian K.

1 Kinoshita T.

1 Reissig M.

1 2003

1 2000

Wyniki wyszukiwania

Representation theorem for the solution of weakly hyperbolic equations with fast oscillating coefficients

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