Scattering operator for nonlinear Klein–Gordon equations in higher space dimensions
| Autor: | Nakao Hayashi, Pavel I. Naumkin |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Applied Mathematics
Mathematical analysis Space (mathematics) Power nonlinearities Higher space dimensions Sobolev space Nonlinear system symbols.namesake Asymptotics of solutions Scattering operator p-Laplacian symbols Nonlinear Klein–Gordon equations Klein–Gordon equation Analysis Trace operator Mathematics Mathematical physics |
| Zdroj: | Journal of Differential Equations. 244(1):188-199 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2007.10.002 |
| Popis: | We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space H β , 1 with β = max ( 3 2 , 1 + 2 n ) for the nonlinear Klein–Gordon equation with a power nonlinearity u t t − Δ u + u = μ | u | σ − 1 u , ( t , x ) ∈ R × R n , where 1 + 4 n + 2 σ 1 + 4 n for n ⩾ 3 , μ ∈ C . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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