estimates for damped wave equations with odd initial data.

Narazaki, Takashi

Displaying similar documents to “ $L^{q}$ estimates for damped wave equations with odd initial data.”

A nonlinear wave equation with a nonlinear integral equation involving the boundary value.

Nguyen, Thanh Long, Bui, Tien Dung (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Blow-up of solutions to a nonlinear wave equation.

Georgiev, Svetlin Georgiev (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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On exact solutions of a degenerate quasilinear wave equation with source term.

Amroun, Nour-Eddine, Benaissa, Abbes (2006)

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

Michael Reissig, Karen Yagdjian (2000)

Banach Center Publications

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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 $u_{t t} - λ^{2} (t) b^{2} (t) (Δ u - m^{2} u) = 0$ . 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).