The Initial Value Problem for the Quadratic Nonlinear Klein-Gordon Equation

Nakao Hayashi and Pavel I. Naumkin

Advances in Mathematical Physics, 2010, vol. 2010, 1-35

Abstract:

We study the initial value problem for the quadratic nonlinear Klein-Gordon equation â„’ ð ‘¢ = ⟨ ð ‘– 𠜕 ð ‘¥ ⟩ − 1 ð ‘¢ 2 , ( ð ‘¡ , ð ‘¥ ) ∈ ð ‘ Ã— ð ‘ , ð ‘¢ ( 0 , ð ‘¥ ) = ð ‘¢ 0 ( ð ‘¥ ) , ð ‘¥ ∈ ð ‘ , where â„’ = 𠜕 ð ‘¡ + ð ‘– ⟨ ð ‘– 𠜕 ð ‘¥ ⟩ and ⟨ ð ‘– 𠜕 ð ‘¥ ⟩ = 1 − 𠜕 2 ð ‘¥ . 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.

Date: 2010
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AMP/2010/504324.pdf (application/pdf)
http://downloads.hindawi.com/journals/AMP/2010/504324.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:504324

DOI: 10.1155/2010/504324

Access Statistics for this article

More articles in Advances in Mathematical Physics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().