Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions
| Autor: | Kota Uriya, Jun Ichi Segata, Satoshi Masaki |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Logarithm
Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Gauge (firearms) 35L71 01 natural sciences Term (time) 010101 applied mathematics symbols.namesake Nonlinear system Range (mathematics) Mathematics - Analysis of PDEs FOS: Mathematics symbols 0101 mathematics Invariant (mathematics) Constant (mathematics) Klein–Gordon equation Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Journal de Mathématiques Pures et Appliquées. 139:177-203 |
| ISSN: | 0021-7824 |
| DOI: | 10.1016/j.matpur.2020.03.009 |
| Popis: | In this paper, we study large time behavior of complex-valued solutions to nonlinear Klein-Gordon equation with a gauge invariant quadratic nonlinearity in two spatial dimensions. To find a possible asymptotic behavior, we consider the final value problem. It turns out that one possible behavior is a linear solution with a logarithmic phase correction as in the real-valued case. However, the shape of the logarithmic correction term has one more parameter which is also given by the final data. In the real case the parameter is constant so one cannot see its effect. However, in the complex case it varies in general. The one dimensional case is also discussed. Comment: 25 papges, 2 figures |
| Databáze: | OpenAIRE |
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