Abstract
Let Ω ⊂ ℝn, n ≥ 2, be an unbounded domain with a smooth (possibly noncompact) star-shaped boundary Γ. For the first mixed problem for a hyperbolic equation with an unbounded coefficient with power growth at infinity, the large-time behavior of the solutions is studied. Estimates for the resolvent of the spectral problem are obtained for various values of the parameters.
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