Generalized energy conservation for klein–gordon type equations

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Abstract

The aim of this paper is to derive energy estimates for solutions of the Cauchy problem for the Klein–Gordon type equation u_(tt) - Δu + m(t)^2u = 0. The coefficient m is given by m(t)^2 = λ(t)^2 + p(t) with a decreasing, smooth shape function λ and an oscillating, smooth and bounded perturbation function p. We study under which assumptions for λ and p one can expect results about a generalization of energy conservation. The main theorems of this note deal with m belonging to C^M, M ≥ 2, and m belonging to the Gevrey class γ^(s), s ≥ 1.

Journal

  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 49(2), 297-323, 2012-06

    Osaka University and Osaka City University, Departments of Mathematics

Codes

  • NII Article ID (NAID)
    120004838783
  • NII NACSIS-CAT ID (NCID)
    AA00765910
  • Text Lang
    ENG
  • Article Type
    departmental bulletin paper
  • ISSN
    0030-6126
  • Data Source
    IR 
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