| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 841257 | Nonlinear Analysis: Theory, Methods & Applications | 2009 | 8 Pages |
Abstract
We study asymptotics around the final states of solutions to the nonlinear Klein–Gordon equations with quadratic nonlinearities in two space dimensions (∂t2−Δ+m2)u=λu2,(t,x)∈R×R2, where λ∈C. We prove that if the final states u1+∈Hqq−14−4q(R2)∩H52,1(R2)∩H12(R2),u2+∈Hqq−13−4q(R2)∩H32,1(R2)∩H11(R2), and ‖u1+‖H12+‖u2+‖H11 is sufficiently small, where 4
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Authors
Nakao Hayashi, Pavel I. Naumkin,