the initial value problem for the quadratic nonlinear klein-gordon equation

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ID: 259891
2010
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Abstract
We study the initial value problem for the quadratic nonlinear Klein-Gordon equation โ„’๐‘ข=โŸจ๐‘–๐œ•๐‘ฅโŸฉโˆ’1๐‘ข2, (๐‘ก,๐‘ฅ)โˆˆ๐‘ร—๐‘, ๐‘ข(0,๐‘ฅ)=๐‘ข0(๐‘ฅ), ๐‘ฅโˆˆ๐‘, where โ„’=๐œ•๐‘ก+๐‘–โŸจ๐‘–๐œ•๐‘ฅโŸฉ and โŸจ๐‘–๐œ•๐‘ฅโŸฉ=1โˆ’๐œ•2๐‘ฅ. Using the Shatah normal forms method, we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.
Reference Key
hayashi2010advancesthe Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Nakao Hayashi;Pavel I. Naumkin
Journal theater
Year 2010
DOI
10.1155/2010/504324
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