空间二维多速半线性Klein-Gordon系统的全局解

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-04-11 DOI:10.1016/j.jde.2025.113279

Xilu Zhu

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引用次数: 0

摘要

考虑二维空间中具有非简并条件的一般半线性多速Klein-Gordon系统。我们证明了在初始数据较小的情况下，这样的解总是全局的，并且分散到一个线性解。这一结果在一定程度上推广了邓[3]的结果，他完整地证明了三维拟线性情况。为了证明我们的结果，我们主要在傅里叶方面进行工作，并探讨了时空共振附近的贡献。

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Global solutions of multispeed semilinear Klein-Gordon systems in space dimension two

We consider general semilinear, multispeed Klein-Gordon systems in space dimension two with some non-degeneracy conditions. We prove that with small initial data such solutions are always global and scatter to a linear solution. This result partly extends the previous result obtained by Deng [3], who completely proved the 3D quasilinear case. To prove our result, we mainly work on Fourier side and explore the contribution from the vicinity of space-time resonance.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics