ISSN:
1432-1785
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The Cauchy Problem for the equation utt−Δu+|u|p−1u=0 (x∈ℝ2, t〉0, ρ〉1) is studied. Smooth Cauchy data is prescribed, and no smallness condition is imposed. For ρ〉5, it is shown that the maximum amplitude of such a wave decays at the expected rate t−1/2 as t→∞. For 1+√8〈ρ≦5, the maximum amplitude still decays, but at a slower rate. These results are then used to demonstrate the existence of the scattering operator when ρ〉ρo, where ρo is the root of the cubic equation ρ3-2ρ2-7ρ-8=0; thus ρo≅4.15.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01170934
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