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Hyperbolic Equations with Growing Coefficients in Unbounded Domains

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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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Authors and Affiliations

  1. N. E. Bauman Moscow State Technical University, Moscow, Russia

    A. V. Filinovskii

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  1. A. V. Filinovskii
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 29, Part II, pp. 455–473, 2013.

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Filinovskii, A.V. Hyperbolic Equations with Growing Coefficients in Unbounded Domains. J Math Sci 197, 435–446 (2014). https://doi.org/10.1007/s10958-014-1725-2

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  • DOI: https://doi.org/10.1007/s10958-014-1725-2

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