Displaying similar documents to “Resolvent estimates and the decay of the solution to the wave equation with potential”

On the uniqueness of ground states of non-local equations

Rupert L. Frank (2011)

Journées Équations aux dérivées partielles

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We review our joint result with E. Lenzmann about the uniqueness of ground state solutions of non-linear equations involving the fractional Laplacian and provide an alternate uniqueness proof for an equation related to the intermediate long-wave equation.

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).