具有Choquard非线性的非局部Klein-Gordon方程的爆破

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-06-11 DOI:10.1007/s00245-025-10280-4

Paulo Cesar Carrião, André Vicente

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引用次数: 0

摘要

本文证明了一类具有非局部Choquard非线性的非局部Klein-Gordon方程的一个爆破结果。此外，我们还证明了与该方程相关的椭圆型问题基态解的不稳定性。为了证明爆炸和不稳定的结果，我们利用波霍扎耶夫流形给出了基态能级的一个新的表征。最后，给出了一个全局存在性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Blow Up for Nonlocal Klein-Gordon Equation with Choquard Nonlinearity

In this paper, we prove a blow-up result for a nonlocal Klein-Gordon equation with a nonlocal Choquard nonlinearity. Additionally, we prove the instability of the ground state solution of the elliptic problem associated with the equation. To prove the blow-up and instability result, using the Pohozaev manifold, we give a new characterization of the ground state level. Finally, we also show a global existence result.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.