| 秦思,王成林,张健.带衰减势的双幂非线性薛定谔方程解的动力学性质[J].数学年刊A辑,2025,46(4):491~516 |
| 带衰减势的双幂非线性薛定谔方程解的动力学性质 |
| Dynamics of the Double Power Nonlinear Schrödinger Equation with Slowly Decaying Potential |
| 投稿时间：2024-06-29 修订日期：2025-12-24 |
| DOI：10.16205/j.cnki.cama.2025.0030 |
| 中文关键词: 非线性薛定谔方程 不变流形 爆破解 质量集中性 极限图景 |
| 英文关键词:The nonlinear Schrödinger equation Invariant manifolds Blow-up solutions Mass concentration Limiting profile |
| 基金项目:国家自然科学基金 (No.12271080) |
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| 摘要点击次数: 108 |
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| 中文摘要: |
| 研究了带有多重物理背景的衰减势的双幂非线性薛定谔方程的柯西问题。通过分析对应的非线性椭圆方程的变分特征，结合方程的质量守恒律和能量守恒律，依据幂指标的不同范围分别给出不同情形下方程的发展不变流及整体与爆破解存在的最佳门槛，同时，根据相关紧性引理，得出柯西问题爆破解在质量临界下的质量集中性、极限图景以及爆破速率下界。 |
| 英文摘要: |
| This paper considers the double power nonlinear Schr?dinger equation with slowly decaying potential possessing multiple physical backgrounds. The invariant manifolds and sharp thresholds are constructed by analyzing the variational characteristics of the corresponding nonlinear elliptic equation, mass conservation and energy conservation and the different range of power exponents. Furthermore, the authors investigate the dynamical properties of blow-up solutions in the critical mass, including mass concentration, limiting profile and rate of blow-up solutions based on relevant compactness lemmas. |
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